These are the sequences that pass recursion tests, but from their definitions it is not clear if they are recursions. I added comments for the sequences that I know not to be recursions. See the main page Recursive Sequences.

- Interesting sequences - I would like to know if they are recurrences or not.
- a(n) = d * a(n-1) - a(n-2).
- a(n) = d * a(n-1) + d * a(n-2).
- a(n) = d * a(n-1) + a(n-2).
- a(n) = a(n-1) + a(n-2).
- a(n) = d * a(n-1). Geometric progressions.
- a(n) = a(n-1) + d. Arithmetic progressions.
- a(n) = a(n-1). Constants.
- Comments.

This page is synchronized with OEIS in January 2007. Sequences in OEIS might start with a different index.

Sequences:

- A123464 a(n) = 2*a(n-1), a(0) = 1.

Number of threshold perfect graphs on n nodes. - A070300 a(n) = a(n-1) + 3, a(0) = 4.

Minimal number of 0's in a 2n X 2n (0,1) matrix that contains no n X n submatrix of 1's. - A085805 a(n) = a(n-1) + 16, a(0) = 4.

Numbers n such that the permanent of the character table of the dihedral group D_n is not zero. - A114142 a(n) = a(n-1) + 1, a(0) = 2.

Possible sums of the final scores of completed Chicago Bears football games. - A114143 a(n) = a(n-1) + 1, a(0) = 4.

The possible sums of the final scores of completed Chicago Bears football games where both teams score. - A118759 a(n) = a(n-1) + 1, a(0) = 0.

A118757(A118757(n)). - A118760 a(n) = a(n-1) + 1, a(0) = 0.

A118758(A118758(n)).

Sequences:

- a(n) = 2a(n-1) - a(n-2). For d = 2 see arithmetic progressions.
- A011783 a(n) = 3*a(n-1) - a(n-2), a(0) = 1, a(1) = 1.

Duplicate of A001519. (dead sequence) - A077461 a(n) = 6*a(n-1) - a(n-2), a(0) = 2, a(1) = 14.

Same as A077444. (dead sequence) - A087096 a(n) = 4*a(n-1) - a(n-2), a(0) = 1, a(1) = 2.

Same as A001075. (dead sequence)

Sequences:

- a(n) = a(n-1) + a(n-2). For d = 1 see a(n) = a(n-1) + a(n-2).
- A085481 a(n) = 3*a(n-1) + 3*a(n-2), a(0) = 1, a(1) = 3.

Same as A030195. (dead sequence)

Sequences:

- A077373 a(n) = a(n-1)+a(n-2), a(0) = 0, a(1) = 1.

Fibonacci numbers whose external digits as well as internal digits form a Fibonacci number.

Non-recursion - subsequence of Fibonacci numbers.

Sequences:

- a(n) = a(n-1) + a(n-2). For d = 1 see a(n) = a(n-1) + a(n-2).
- A048624 a(n) = 2*a(n-1)+a(n-2), a(0) = 2, a(1) = 5.

Essentially a duplicate of A000129. (dead sequence) - A084133 a(n) = 6*a(n-1)+a(n-2), a(0) = 1, a(1) = 3.

Duplicate of A005667. (dead sequence)

Sequences:

- a(n) = a(n-1). For d = 1 see constants.
- A025489 a(n) = 2*a(n-1), a(0) = 2.

Numbers on backgammon doubling cube.

Finite sequence - non recursive. - A060365 a(n) = 1000*a(n-1), a(0) = 1.

Multiples of one million which are described by single words in American English.

Finite sequence - non recursive. - A060366 a(n) = 1000*a(n-1), a(0) = 1.

Multiples of one million which are described by single words in British English.

Finite sequence - non recursive. - A067482 a(n) = 1024*a(n-1), a(0) = 4.

Powers of 4 with initial digit 4. - A067484 a(n) = 10077696*a(n-1), a(0) = 6.

Powers of 6 with initial digit 6. - A121499 a(n) = 841*a(n-1), a(0) = 1.

Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841.

Non recursive. Comment by Max Alekseyev: The recurrent formula fails as soon as C(n) is divisible by 29. First time it happens for n=15. - A123464 a(n) = 2*a(n-1), a(0) = 1.

Number of threshold perfect graphs on n nodes. - A125581 a(n) = 11*a(n-1), a(0) = 77.

Numbers n such that n does not divide the denominator of the n-th harmonic number nor the denominator of the n-th alternating harmonic number.

Non-recursive. Comment by Max Alekseyev: While A125581 indeed contains the geometric progression 7*11^{n}as a subsequence, it also contains other geometric progressions such as: 506*1093^{n}, 1092*1093^{n}, 1755*3511^{n}, 3510*3511^{n}, and 4896*5557^{n}.

Sequences:

- a(n) = a(n-1). For d = 0 see constants.
- A004924 a(n) = a(n-1) + 76, a(0) = 0.

Floor of n*tau^9. - A004926 a(n) = a(n-1) + 199, a(0) = 0.

Floor of n*tau^11. - A004928 a(n) = a(n-1) + 521, a(0) = 0.

Floor of n*tau^13. - A004930 a(n) = a(n-1) + 1364, a(0) = 0.

Floor of n*tau^15. - A004932 a(n) = a(n-1) + 3571, a(0) = 0.

Floor of n*tau^17. - A004934 a(n) = a(n-1) + 9349, a(0) = 0.

Floor of n*tau^19. - A004944 a(n) = a(n-1) + 76, a(0) = 0.

Nearest integer to n*tau^9. - A004945 a(n) = a(n-1) + 123, a(0) = 0.

Nearest integer to n*tau^10. - A004946 a(n) = a(n-1) + 199, a(0) = 0.

Nearest integer to n*tau^11. - A004947 a(n) = a(n-1) + 322, a(0) = 0.

Nearest integer to n*tau^12. - A004948 a(n) = a(n-1) + 521, a(0) = 0.

Nearest integer to n*tau^13. - A004949 a(n) = a(n-1) + 843, a(0) = 0.

Nearest integer to n*tau^14. - A004950 a(n) = a(n-1) + 1364, a(0) = 0.

Nearest integer to n*tau^15. - A004951 a(n) = a(n-1) + 2207, a(0) = 0.

Nearest integer to n*tau^16. - A004952 a(n) = a(n-1) + 3571, a(0) = 0.

Nearest integer to n*tau^17. - A004953 a(n) = a(n-1) + 5778, a(0) = 0.

Nearest integer to n*tau^18. - A004954 a(n) = a(n-1) + 9349, a(0) = 0.

Nearest integer to n*tau^19. - A004955 a(n) = a(n-1) + 15127, a(0) = 0.

Nearest integer to n*tau^20. - A004963 a(n) = a(n-1) + 47, a(0) = 0.

Ceiling of n*tau^8. - A004965 a(n) = a(n-1) + 123, a(0) = 0.

Ceiling of n*tau^10. - A004967 a(n) = a(n-1) + 322, a(0) = 0.

Ceiling of n*tau^12. - A004969 a(n) = a(n-1) + 843, a(0) = 0.

Ceiling of n*tau^14. - A004971 a(n) = a(n-1) + 2207, a(0) = 0.

Ceiling of n*tau^16. - A004973 a(n) = a(n-1) + 5778, a(0) = 0.

Ceiling of n*tau^18. - A004975 a(n) = a(n-1) + 15127, a(0) = 0.

Ceiling of n*tau^20. - A008553 a(n) = a(n-1) + 1, a(0) = 20.

Numbers that contain the letter `y'.

Non recursive. - A017149 a(n) = a(n-1) + 8, a(0) = 7.

Same as A004771. (dead sequence) - A031193 a(n) = a(n-1) + 3, a(0) = 3.

Numbers having period-22 5-digitized sequences.

Non recursive. - A032614 a(n) = a(n-1) + 101, a(0) = 110.

Concatenation of n and n + 9 or {n,n+9}.

Non recursive. - A033168 a(n) = a(n-1) + 210, a(0) = 199.

Longest arithmetic progression of primes with difference 210 and minimal initial term.

Finite sequence - non recursive. - A033290 a(n) = a(n-1) + 210, a(0) = 100996972469714247637786655587969840329509324689190041803603417758904341703348882159067229719.

Ten consecutive primes in arithmetic progression.

Finite sequence - non recursive. - A044138 a(n) = a(n-1) + 49, a(0) = 49.

Numbers n such that string 0,0 occurs in the base 7 representation of n but not of n-1.

Non recursive. See Comment. - A044179 a(n) = a(n-1) + 49, a(0) = 41.

Numbers n such that string 5,6 occurs in the base 7 representation of n but not of n-1.

Non recursive. See Comment. - A044187 a(n) = a(n-1) + 64, a(0) = 64.

Numbers n such that string 0,0 occurs in the base 8 representation of n but not of n-1.

Non recursive. See Comment. - A044242 a(n) = a(n-1) + 64, a(0) = 55.

Numbers n such that string 6,7 occurs in the base 8 representation of n but not of n-1.

Non recursive. See Comment. - A044251 a(n) = a(n-1) + 81, a(0) = 81.

Numbers n such that string 0,0 occurs in the base 9 representation of n but not of n-1.

Non recursive. See Comment. - A044322 a(n) = a(n-1) + 81, a(0) = 71.

Numbers n such that string 7,8 occurs in the base 9 representation of n but not of n-1.

Non recursive. See Comment. - A044332 a(n) = a(n-1) + 100, a(0) = 100.

Numbers n such that string 0,0 occurs in the base 10 representation of n but not of n-1.

Non recursive. See Comment. - A044421 a(n) = a(n-1) + 100, a(0) = 89.

Numbers n such that string 8,9 occurs in the base 10 representation of n but not of n-1.

Non recursive. See Comment. - A044567 a(n) = a(n-1) + 49, a(0) = 48.

Numbers n such that string 6,6 occurs in the base 7 representation of n but not of n+1.

Non recursive. See Comment. - A044631 a(n) = a(n-1) + 64, a(0) = 63.

Numbers n such that string 7,7 occurs in the base 8 representation of n but not of n+1.

Non recursive. See Comment. - A044712 a(n) = a(n-1) + 81, a(0) = 80.

Numbers n such that string 8,8 occurs in the base 9 representation of n but not of n+1.

Non recursive. See Comment. - A044812 a(n) = a(n-1) + 100, a(0) = 99.

Numbers n such that string 9,9 occurs in the base 10 representation of n but not of n+1.

Non recursive. See Comment. - A046050 a(n) = a(n-1) + 80, a(0) = 79.

Sum of 19 but no fewer nonzero fourth powers.

Finite sequence - non recursive. - A047738 a(n) = a(n-1) + 1, a(0) = 179210312.

Earliest sequence of 4 consecutive economical numbers.

Finite sequence - non recursive. - A050518 a(n) = a(n-1) + 583200, a(0) = 583200.

Arithmetic progression of at least 6 terms having the same value of phi start at these numbers.

Non-recursive. Comment by Max Alekseyev: a(3888)=3889*583200 does NOT belong to A050518. - A050519 a(n) = a(n-1) + 30, a(0) = 30.

Increments of arithmetic progression of at least 6 terms having the same value of phi in A050518. - A058908 a(n) = a(n-1) + 9876543210, a(0) = 5077.

Six prime numbers in arithmetical progression with a common difference of 9876543210.

Finite sequence - non recursive. - A059558 a(n) = a(n-1) + 4, a(0) = 4.

Beatty sequence for 1+1/gamma^2.

Non recursive. Comment by Max Alekseyev: a first counterexample to recurrence is a(715)=2861. - A069782 a(n) = a(n-1) + 1, a(0) = 1.

Numbers n such that g[n] := GCD[d[n^3],d[n]] = 2^w for some w. The first missing integer is 432 (See in A069781).

Non recursive. - A070300 a(n) = a(n-1) + 3, a(0) = 4.

Minimal number of 0's in a 2n X 2n (0,1) matrix that contains no n X n submatrix of 1's. - A074337 a(n) = a(n-1) + 9922782870, a(0) = 107928278317.

18 primes in arithmetic progression.

Finite sequence - non recursive. - A081734 a(n) = a(n-1) + 30, a(0) = 121174811.

First and smallest sequence of 6 consecutive primes in arithmetic progression.

Finite sequence - non recursive. - A082221 a(n) = a(n-1) + 6, a(0) = 1.

In the following square array numbers (not occurring earlier) are entered like this a(1,1),a(1,2),a(2,1),a(3,1),a(2,2),a(1,3),a(1,4),a(2,3),a(3,2),a(4,1),a(5,1),a(4,2),... such that every n-th partial sum of a row or a column is a multiple of n. 1 3 2 10 19 25... 5 7 12 16 15... 6 8 13 37... 4 14 18... 9 23... 11... ... Sequence contains the main diagonal.

Non recursive - more terms calculated by Max Alekseyev. - A082249 a(n) = a(n-1) + 7070707070707, a(0) = 22212019181716.

Reverse concatenation of 7 numbers that are multiples of 7.

Non recursive. Comment by Max Alekseyev: The next term of A082249 is 108107106105104103102 and it does NOT satisfy the recurrent formula. - A082946 a(n) = a(n-1) + 101, a(0) = 111.

Palindromes satisfying A082945.

Non recursive. Comment by Max Alekseyev: if it were a recursive sequence then the next (currently unlisted) term would be 919+101=1020 which is not a palindrome. - A085805 a(n) = a(n-1) + 16, a(0) = 4.

Numbers n such that the permanent of the character table of the dihedral group D_n is not zero. - A088475 a(n) = a(n-1) + 1, a(0) = 10.

Numbers n such that dismal sum of prime divisors of n is ≥ n.

Non-recursive. - A088480 a(n) = a(n-1) + 1, a(0) = 1.

Numbers n such that dismal product of prime divisors of n is ≥ n.

Non-recursive. Complement of A088477 - A096582 a(n) = a(n-1) - 1, a(0) = 100.

From the "100 Green Bottles" song.

Finite sequence - non recursive. - A103303 a(n) = a(n-1) + 1, a(0) = 0.

Complete list of digits used in the counting numbers (in base 10). Also known as the "arabic numerals".

Finite sequence - non recursive. - A104340 a(n) = a(n-1) + 11, a(0) = 12.

Numbers n such that (digital reversal of n) - n = 9.

Finite sequence - non recursive. - A104341 a(n) = a(n-1) + 11, a(0) = 10.

Numbers n such that n -(digital reversal of n) = 9.

Finite sequence - non recursive. - A104342 a(n) = a(n-1) + 11, a(0) = 13.

Numbers n such that (digital reversal of n) - n = 18.

Finite sequence - non recursive. - A107843 a(n) = a(n-1) - 2, a(0) = 201.

Number of iterations of McCarthy 91 Function until it terminates.

Non recursive. - A109065 a(n) = a(n-1) - 1, a(0) = 12.

Numerator of the fraction due in month n of the total interest for a one-year installment loan based on the Rule of 78s (Each denominator is 78).

Finite sequence - non recursive. - A109632 a(n) = a(n-1) + 300, a(0) = 200.

In the game of bridge, a(n) is the penalty for going down n tricks in a vulnerable, doubled contract.

Finite sequence - non recursive. - A112821 a(n) = a(n-1) + 1, a(0) = 343.

Numbers n such that 19*LCM(1,2,3,...,n) equals the denominator of the n-th harmonic number H(n).

Non recursive. Comment by Max Alekseyev: 361 does not belong to A112821. - A114142 a(n) = a(n-1) + 1, a(0) = 2.

Possible sums of the final scores of completed Chicago Bears football games. - A114143 a(n) = a(n-1) + 1, a(0) = 4.

The possible sums of the final scores of completed Chicago Bears football games where both teams score. - A115020 a(n) = a(n-1) - 7, a(0) = 100.

Count backwards from 100 in steps of 7.

Finite sequence - non recursive. - A115536 a(n) = a(n-1) + 9434, a(0) = 160378.

Numbers n such that the square of n is the concatenation of two numbers m and 4*m. - A115548 a(n) = a(n-1) + 30434782608695652173913043478260869565217391304347826087, a(0) = 91304347826086956521739130434782608695652173913043478261.

Numbers n such that the square of n is the concatenation of two numbers m and 7*m. - A118759 a(n) = a(n-1) + 1, a(0) = 0.

A118757(A118757(n)). - A118760 a(n) = a(n-1) + 1, a(0) = 0.

A118758(A118758(n)). - A120420 a(n) = a(n-1) + 1, a(0) = 2.

Numbers n such that n! is highly composite (in the sense of A002182).

Non recursive. - A121377 a(n) = a(n-1) + 1, a(0) = 48.

ASCII codes for decimal digits.

Finite sequence - non recursive. - A121378 a(n) = a(n-1) + 1, a(0) = 240.

EBCDIC codes for decimal digits.

Finite sequence - non recursive.

Sequences:

- A058445 a(n) = 2236081408416666.

Numbers n such that n^2 contains only digits {0,5,6}, not ending with zero.

Contains only one number - non recursive. - A058446 a(n) = 5000060065066660656065066555556.

Squares composed of digits {0,5,6}, not ending with zero.

Contains only one number - non recursive. - A072288 a(n) = 316912650057057350374175801344000001.

Smallest prime factor of Googolplex + n which exceeds 16.

Contains only one number - non recursive. - A076337 a(n) = 509203.

Riesel numbers: n such that for all k ≥ 1 the numbers n*2^k - 1 are composite.

Contains only one number - non recursive. - A082710 a(n) = 10907.

Plateau and depression primes of the form (10^a(n)-1)/9+6*(10^[ a(n)-1 ]+1) or (64*10^[ a(n)-1 ]+53)/9.

Contains only one number - non recursive. - A115453 a(n) = 1414213562373095048801688724209698078569671875376948073.

Numbers n such that the first n digits of Sqrt[2] form a prime.

Contains only one number - non recursive. - A118329 a(n) = 9159655941772190150546035149323841107741493742816721.

Catalan-primes: primes formed from the concatenation of initial decimal digits of Catalan's constant.

Contains only one number - non recursive.

- The following comment was sent to me by Max Alekseyev. All sequences of the type "Numbers n such that string x,y occurs in the base b representation of n but not of n-1" are not recursive.
- If x=y=0 then the first deviation is b
^{4}+b^{2}=b^{2}*(b^{2}+1). - If x=y is non-zero then the first deviation is x*(b
^{2}+b+1). - If x and y are distinct then the first deviation is x*b
^{3}+y*b^{2}+x*b+y=(x*b+y)*(b^{2}+1).

- If x=y=0 then the first deviation is b

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Contact me: Tanya Khovanova

tanyakh@yahoo.com

Last revised March 2007