A391253 Odd semiprimes p*q such that either p*q = A048720(p,x) or p*q = A048720(q,x) for some x, where A048720 is the carryless binary multiplication.

9, 15, 21, 33, 35, 39, 49, 51, 57, 65, 85, 93, 95, 111, 119, 123, 129, 133, 141, 155, 159, 161, 177, 183, 187, 201, 215, 217, 219, 221, 235, 237, 249, 259, 267, 287, 291, 303, 309, 335, 341, 365, 371, 381, 393, 403, 411, 413, 417, 427, 447, 469, 485, 489, 497, 511, 519, 527, 537, 543, 573, 579, 589, 591, 597, 611

Offset

1,1

Comments

Question: How does ratio a(n)/A391254(n) grow?

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_A391253(n) = if(!(n%2) || 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, A280500, A391254 (complement among A046315).

Subsequences: A365473, semiprimes of A391248, A391255, A391328 (terms that are not multiples of 3).

Similar sequences: A391257, A391343, A391333 (analogous sequence for the carryless base-3 multiplication).

Sequence in context: A395349 A061254 A175626 * A391336 A391257 A096788

Adjacent sequences: A391250 A391251 A391252 * A391254 A391255 A391256

Keyword

nonn,base

Author

Antti Karttunen, Dec 06 2025

Status

approved