A391331 Odd semiprimes k = p*q such that k = A325820(p,q), with p, q primes > 3, and A325820 is the carryless base-3 multiplication.

377, 403, 481, 961, 1079, 1199, 1355, 1369, 1417, 1897, 2071, 2119, 2573, 3071, 3379, 3523, 3695, 3785, 4033, 4055, 5053, 5173, 5299, 5677, 6031, 6331, 8063, 8327, 8401, 9529, 9607, 9841, 10027, 10543, 10907, 11345, 11881, 12869, 13117, 13927, 14383, 15097, 15883, 17411, 18019, 18967, 19331, 19357, 21257, 21431

Offset

1,1

Comments

Terms of A391332 that are not multiples of 3.

Links

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

Index entries for sequences related to carryless arithmetic.

Example

961 = 31*31 and A007089(31) = 1011, and when doing a long multiplication of 1011 x 1011 we obtain:
     1011
    1011
  1011
  -------
  1022121 = A007089(961), without any carries occurring (all summands stay < 3), therefore 961 is included as a term.

Prog

(PARI)
A325820_sq(b, c) = fromdigits(Vec(Pol(digits(b, 3))*Pol(digits(c, 3)))%3, 3);
is_A391331(n) = if(!(n%2) || !(n%3) || 2!=bigomega(n), 0, my(f=factor(n), a = f[1, 1], b = f[#f~, 1]); (A325820_sq(a, b)==n));

Crossrefs

Intersection of A001651 and A391332.

Subsequence of A391330, and of A391335.

Cf. A007089, A325820.

Sequence in context: A198640 A171489 A105717 * A352264 A222350 A277942

Adjacent sequences: A391328 A391329 A391330 * A391332 A391333 A391334

Keyword

nonn,base

Author

Antti Karttunen, Dec 07 2025

Status

approved