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

1,2

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

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 *)

Prog

(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

Crossrefs

Cf. A001006, A081736.

Sequence in context: A330123 A354711 A140826 * A373142 A227231 A107036

Adjacent sequences: A081732 A081733 A081734 * A081736 A081737 A081738

Keyword

nonn

Author

Benoit Cloitre, Apr 06 2003

Extensions

First term 1 prepended by Altug Alkan, Jan 07 2016

Status

approved