A391737 Numbers k such that 25*k = A048720(25, k), where A048720 is carryless base-2 multiplication.

0, 1, 2, 4, 5, 8, 10, 16, 20, 32, 33, 40, 64, 65, 66, 80, 128, 129, 130, 132, 133, 160, 161, 256, 257, 258, 260, 261, 264, 266, 320, 321, 322, 512, 513, 514, 516, 517, 520, 522, 528, 532, 640, 641, 642, 644, 645, 1024, 1025, 1026, 1028, 1029, 1032, 1034, 1040, 1044, 1056, 1057, 1064, 1280, 1281, 1282, 1284, 1285

Offset

1,3

Comments

Numbers k such that k XOR 8*k XOR 16*k = 25*k.

If n is a term, then 2*n is also a term, and vice versa.

Links

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

Index entries for sequences defined by congruent products between domains N and GF(2)[X].

Index entries for sequences related to binary expansion of n.

Index entries for sequences related to carryless arithmetic.

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
is_A391737(k) = (25*k == A048720(25, k));
(PARI) is_A391737(n) = (bitxor(n, bitxor(8*n, 16*n))==25*n);

Crossrefs

Cf. A048720.

Subsequence of A115831. The first terms that occur in A115831 but not here are 143, 285, and 286.

Subsequence of A391858.

Cf. also A115422, and A391738, A391739.

Sequence in context: A018433 A228939 A115831 * A094958 A018565 A018391

Adjacent sequences: A391734 A391735 A391736 * A391738 A391739 A391740

Keyword

nonn,base

Author

Antti Karttunen, Dec 21 2025

Status

approved