A391328 Odd semiprimes k = p*q, p, q primes > 3, such that either k = A048720(p,x) or k = A048720(q,x) for some x, where A048720 is the carryless binary multiplication.

35, 49, 65, 85, 95, 119, 133, 155, 161, 187, 215, 217, 221, 235, 259, 287, 335, 341, 365, 371, 403, 413, 427, 469, 485, 497, 511, 527, 589, 611, 629, 635, 655, 679, 685, 689, 697, 713, 745, 781, 791, 793, 889, 899, 913, 917, 959, 961, 965, 1055, 1057, 1115, 1139, 1141, 1145, 1195, 1205, 1241, 1253, 1285, 1337, 1345

Offset

1,1

Comments

Terms of A391253 without any multiples of 3.

Links

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

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to carryless arithmetic.

Prog

(PARI) is_A391328(n) = if(!(n%2) || !(n%3) || 2!=bigomega(n), 0, my(f=factor(n), a = f[1, 1], b = f[#f~, 1], Pa=Pol(binary(a))*Mod(1, 2), Pb=Pol(binary(b))*Mod(1, 2), Pn=Pol(binary(n))*Mod(1, 2)); ((0==lift(Pn % Pa)) || (0==lift(Pn % Pb))));

Crossrefs

Cf. A048720.

Intersection of A001651 and A391253.

Subsequence of A391330.

Cf. A391335 (analogous sequence for the carryless base-3 multiplication).

Sequence in context: A034115 A212600 A247135 * A249819 A391329 A186319

Adjacent sequences: A391325 A391326 A391327 * A391329 A391330 A391331

Keyword

nonn,base

Author

Antti Karttunen, Dec 07 2025

Status

approved