A391338 Numbers k such that Stern polynomial B(3*k,x) is equal to B(3,x) * B(k,x).

1, 2, 3, 4, 6, 8, 9, 12, 13, 16, 18, 23, 24, 26, 32, 35, 36, 46, 48, 51, 52, 59, 64, 70, 72, 73, 79, 92, 93, 96, 102, 104, 105, 118, 128, 140, 141, 144, 146, 158, 183, 184, 186, 192, 204, 205, 208, 210, 236, 256, 279, 280, 282, 288, 291, 292, 316, 366, 368, 371, 372, 384, 407, 408, 410, 416, 419, 420, 472, 512

Offset

1,2

Comments

Positions of nonzero terms on the third row of array A391260.

If n is present, then 2*n is also present, and vice versa.

Links

Antti Karttunen, Table of n, a(n) for n = 1..3094

Prog

(PARI)
memo_for_ps = Map();
ps(n) = if(n<2, n, my(v); if(mapisdefined(memo_for_ps, n, &v), v, v = if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)); if(n%2, mapput(memo_for_ps, n, v)); (v))); \\ Only memoize on odd n...
is_A391338(n) = (ps(3*n)==ps(3)*ps(n));

Crossrefs

Cf. A391260, A391339 (complement), A391340 (odd terms).

Cf. A125184, A260443 for a description of Stern polynomials.

Cf. also A391348.

Sequence in context: A071403 A010407 A035240 * A278580 A028929 A308299

Adjacent sequences: A391335 A391336 A391337 * A391339 A391340 A391341

Keyword

nonn

Author

Antti Karttunen, Dec 08 2025

Status

approved