A391742 Numbers k such that 7*k = A048720(m, k) for some m, where A048720 is carryless base-2 multiplication.

0, 1, 2, 4, 7, 8, 9, 14, 15, 16, 17, 18, 28, 30, 31, 32, 33, 34, 36, 56, 60, 62, 63, 64, 65, 66, 68, 72, 73, 112, 120, 124, 126, 127, 128, 129, 130, 132, 136, 137, 144, 145, 146, 224, 240, 248, 252, 254, 255, 256, 257, 258, 260, 264, 265, 272, 273, 274, 288, 289, 290, 292, 448, 455, 480, 496, 504, 508, 510, 511, 512, 513

Offset

1,3

Comments

If n is a term, then 2*n is also a term, and vice versa. See A391743 for the odd terms.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

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.

Formula

{0 followed by k such that A280500(7*k, k) = m for some m > 0}.

Example

7 is a term as 7*7 = A048720(7,11), i.e., A280500(49,7) = 11.
9 is a term as 7*9 = A048720(7,9), i.e., A280500(63,9) = 7.

Prog

(PARI) is_A391742(k) = (!k || (0==lift(Pol(binary(7*k)*Mod(1, 2)) % Pol(binary(k))*Mod(1, 2))));

Crossrefs

Cf. A048720, A280500.

Row 7 of A391925.

Subsequences: A048715 (m=7), A115770 (m=11), A391743 (odd terms).

Cf. also A391585, A391740, A391744.

Sequence in context: A182636 A116724 A391346 * A035251 A391348 A141401

Adjacent sequences: A391739 A391740 A391741 * A391743 A391744 A391745

Keyword

nonn,base

Author

Antti Karttunen, Dec 21 2025

Status

approved