A391343 Odd semiprimes k = p*q such that either k = A048720(A065621(p),x) or k = A048720(A065621(q),x) for some x.

9, 21, 33, 35, 49, 65, 93, 129, 133, 155, 161, 217, 259, 287, 309, 341, 381, 403, 527, 589, 597, 611, 635, 681, 699, 713, 785, 793, 849, 871, 889, 899, 923, 961, 1047, 1055, 1057, 1101, 1119, 1299, 1317, 1345, 1371, 1379, 1389, 1397, 1461, 1477, 1497, 1623, 1631, 1651, 1707, 1745, 1765, 1795, 1857, 1893, 2045, 2049

Offset

1,1

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.

Index entries for sequences related to polynomials in ring GF(2)[X].

Prog

(PARI)
A065621(n) = bitxor(n-1, n+n-1);
is_A391343(n) = if(!(n%2) || 2!=bigomega(n), 0, my(f=factor(n), a = A065621(f[1, 1]), b = A065621(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

Setwise difference A046315 \ A391344.

Cf. A048720, A065621, A391248 (semiprimes in that sequence is a subsequence of this one).

Cf. also A391253.

Sequence in context: A243703 A133929 A325573 * A086470 A176256 A017629

Adjacent sequences: A391340 A391341 A391342 * A391344 A391345 A391346

Keyword

nonn

Author

Antti Karttunen, Dec 07 2025

Status

approved