A081735 Numbers k such that the k-th Motzkin number == 1 (mod k).

1, 3, 4, 5, 7, 11, 13, 17, 19, 23, 25, 29, 30, 31, 37, 41, 43, 47, 49, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257

Offset: 1

Author

Benoit Cloitre, Apr 06 2003

Keywords

• nonn

Comments

All odd primes and all squares of primes are in the sequence. First composite (and not square of prime) are : 30, 464, 902, 21475, ... (A081736). [Scott R. Shannon points out that this comment is wrong, since 9 is missing. Are there other errors? The comment needs to checked and corrected. - N. J. A. Sloane, Dec 15 2022]

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001006, A081736.

Programs

Mathematica

motzkin[0] = 1; motzkin[n_] := motzkin[n] = motzkin[n - 1] + Sum[motzkin[k] * motzkin[n - k - 2], {k, 0, n - 2}]; Select[Range[250], # == 1 || Mod[motzkin[#], #] == 1 &] (* Amiram Eldar, May 23 2022 *)

PARI

a001006(n) = polcoeff((1-x-sqrt((1-x)^2-4*x^2+x^3*O(x^n)))/(2*x^2), n);
for(n=1, 1e3, if((a001006(n)-1) % n == 0, print1(n, ", "))); \\ Altug Alkan, Jan 07 2016

Extensions

First term 1 prepended by Altug Alkan, Jan 07 2016