A391568 Numbers k for which there exists an integer m in range k+1 .. A065621(k)-1 and an odd number i <= k^3 such that m*i = A048720(k, i), where A048720 is carryless base-2 multiplication.

19, 21, 23, 27, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 51, 54, 55, 59, 67, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94, 95, 99, 101, 102, 103, 105, 107, 108, 109, 110, 111, 115, 118, 119, 123, 131, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 145, 146, 147, 148, 149

Offset

1,1

Comments

Indices i where A065621(i) differs from A115857(i), or equally, indices i where A115873(i) differs from A391567(i).

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..123

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

{k | A065621(k) != A115857(k)}.

Example

For n = 19, A115857(19) = 23 and A391567(19) = 3, and we have A048720(3,23) = 57 = 19*3, and because 19 < A115857(19) = 23 < A065621(19) = 55, and 3 <= 19^3, 19 is included in this sequence.

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A065621(n) = bitxor(n-1, n+n-1);
A209229(n) = (n && !bitand(n, n-1));
is_A391568(k) = { for(m=k+1, A065621(k)-1, forstep(i=1, k^3, 2, if((k*i)==A048720(m, i), return(1)))); (0); };

Crossrefs

Cf. A048720, A065621, A115857, A115873, A391567.

Sequence in context: A020347 A334103 A347343 * A054864 A158232 A178889

Adjacent sequences: A391565 A391566 A391567 * A391569 A391570 A391571

Keyword

nonn,base

Author

Antti Karttunen, Dec 15 2025

Status

approved