A391567 If n is a power of 2, then a(n) = 1, otherwise we search for the smallest integer m > n, for which there exists an odd number i <= n^3 such that m*i = A048720(n, i), and return that i as the result of a(n). Here A048720 is carryless base-2 multiplication.

1, 1, 3, 1, 7, 3, 7, 1, 15, 7, 3, 3, 5, 7, 15, 1, 31, 15, 3, 7, 5, 3, 45, 3, 31, 5, 2295, 7, 31, 15, 31, 1, 63, 31, 3, 15, 45, 3, 5, 7, 7, 5, 5, 3, 5, 45, 5, 3, 21, 31, 17391, 5, 63, 2295, 17391, 7, 9, 31, 1079, 15, 21, 31, 63, 1, 127, 63, 3, 31, 7, 3, 7, 15, 9, 45, 55269, 3, 3, 5, 3, 7, 21, 7, 3, 5, 765, 5, 11, 3

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..207

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

For all n >= 1, n * a(n) = A048720(A115857(n), a(n)).

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));
A391567(n) = if(A209229(n), 1, for(m=n+1, A065621(n), forstep(i=1, n^3, 2, if((n*i)==A048720(m, i), return(i)))); (0));

Crossrefs

Cf. A048720, A115857 (gives the corresponding number m).

Differs from A115873 at positions given by A391568.

Cf. also A391570, A391572.

Sequence in context: A247675 A053092 A212045 * A292849 A115873 A329369

Adjacent sequences: A391564 A391565 A391566 * A391568 A391569 A391570

Keyword

nonn

Author

Antti Karttunen, Dec 15 2025

Status

approved