A391329 Odd semiprimes p*q, p, q > 3, such that Stern polynomial B(p*q,x) is a multiple of either B(p,x) or B(q,x).

35, 49, 85, 119, 155, 187, 217, 221, 259, 287, 341, 355, 365, 371, 403, 413, 437, 497, 511, 527, 535, 553, 565, 589, 611, 635, 685, 713, 745, 791, 793, 835, 871, 889, 899, 901, 923, 959, 961, 1073, 1115, 1195, 1205, 1261, 1285, 1315, 1355, 1385, 1397, 1561, 1651, 1673, 1679, 1685, 1687, 1691, 1703, 1745, 1757, 1799

Offset

1,1

Comments

Terms of A391257 without any multiples of 3.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

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_A391329(n) = if(!(n%2) || !(n%3) || 2!=bigomega(n), 0, my(f=factor(n), a = f[1, 1], b = f[#f~, 1], Pa = ps(a), Pb = if(b==a, Pa, ps(b)), Pn = ps(n)); (0==lift(Pn % Pa) || 0==lift(Pn % Pb)));

Crossrefs

Intersection of A001651 and A391257. Also a subsequence of A391330 and of A391336.

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

Sequence in context: A247135 A391328 A249819 * A186319 A248659 A089268

Adjacent sequences: A391326 A391327 A391328 * A391330 A391331 A391332

Keyword

nonn

Author

Antti Karttunen, Dec 08 2025

Status

approved