A391573 a(n) is the value of quotient A048720(n,k)/k for the smallest odd k > 1 for which A048720(n,k) is a multiple of k (in ordinary arithmetic), where A048720 is carryless base-2 multiplication.

1, 2, 3, 4, 5, 6, 3, 8, 9, 10, 7, 12, 5, 6, 15, 16, 17, 18, 19, 20, 21, 14, 19, 24, 25, 10, 15, 12, 13, 30, 11, 32, 33, 34, 35, 36, 37, 38, 35, 40, 41, 42, 27, 28, 45, 38, 27, 48, 49, 50, 51, 20, 45, 30, 47, 24, 25, 26, 43, 60, 21, 22, 39, 64, 65, 66, 67, 68, 69, 70, 67, 72, 73, 74, 71, 76, 69, 70, 63, 80, 81, 82, 63

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

a(n) * A391572(n) = A048720(n, A391572(n)).

a(n) <= n. [Implied by above, as x*y >= A048720(x,y)]

a(A003714(n)) = A003714(n). [A003714 is a proper subset of fixed points, A391579]

Prog

(PARI)
A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);
A391573(n) = { my(t); forstep(k=3, oo, 2, if(!((t=A048720(n, k))%k), return(t/k))); };

Crossrefs

Cf. A003714, A048720, A391569 (= n XOR a(n)), A391572, A391578 (k such that a(k) < k), A391579 (fixed points).

Column 2 of A391736.

Cf. also A391570, A391571.

Sequence in context: A096894 A097751 A070667 * A374056 A245349 A122416

Adjacent sequences: A391570 A391571 A391572 * A391574 A391575 A391576

Keyword

nonn,base

Author

Antti Karttunen, Dec 16 2025

Status

approved