A391585 Numbers k such that 3*k = A048720(m,k) for some m, where A048720 is carryless base-2 multiplication.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 20, 21, 24, 28, 30, 31, 32, 33, 34, 36, 37, 40, 41, 42, 48, 51, 56, 60, 62, 63, 64, 65, 66, 68, 69, 72, 73, 74, 80, 81, 82, 84, 85, 96, 99, 102, 103, 112, 115, 120, 124, 126, 127, 128, 129, 130, 132, 133, 136, 137, 138, 144, 145, 146, 148, 149, 160, 161, 162, 164, 165

Offset

1,3

Comments

If n is a term, then 2*n is also a term, and vice versa. See A391584 for 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.

Prog

(PARI) is_A391585(k) = (!k || (0==lift(Pol(binary(3*k)*Mod(1, 2)) % Pol(binary(k))*Mod(1, 2))));
(PARI)
up_to = 10001;
A391585list(up_to_n) = { my(v=vector(up_to_n), k=1, i=0); v[1] = 0; while(k<#v, i++; my(P3i=Pol(binary(3*i))*Mod(1, 2), P_i=Pol(binary(i))*Mod(1, 2)); if(0==lift(P3i % P_i), k++; v[k] = i)); (v); };
v391585 = A391585list(up_to);
A391585(n) = v391585[n];

Crossrefs

Row 3 of A391925.

Cf. A048720, A280500.

Subsequences: A003714 (m=3), A048717 (m=7), A391584 (odd terms).

Different from A125121, A295235 and A333762.

Cf. also other rows of A391925: A391740 (row 5), A391742 (row 7), A391744 (row 9), A391846 (row 11), A391848 (row 13), A391850 (row 15), A391852 (row 17), A391854 (row 19), A391856 (row 21), A391858 (row 25), A391860 (row 49).

Sequence in context: A057890 A161604 A125121 * A333762 A295235 A136490

Adjacent sequences: A391582 A391583 A391584 * A391586 A391587 A391588

Keyword

nonn,base

Author

Antti Karttunen, Dec 18 2025

Status

approved