A391582 - OEIS

A391582

a(n) is the third odd number k such that k*n = A048720(k,m) for some m, where A048720 is carryless base-2 multiplication.

5, 5, 5, 5, 7, 5, 9, 5, 5, 7, 15, 5, 5, 9, 5, 5, 5, 5, 5, 7, 5, 15, 31, 5, 5, 5, 7, 9, 33, 5, 33, 5, 5, 5, 5, 5, 7, 5, 7, 7, 7, 5, 5, 15, 5, 31, 5, 5, 5, 5, 5, 5, 7, 7, 7, 9, 9, 33, 7, 5, 7, 33, 7, 5, 5, 5, 5, 5, 7, 5, 9, 5, 5, 7, 17, 5, 9, 7, 15, 7, 7, 7, 11, 5, 9, 5, 21, 15, 9, 5, 9, 31, 23, 5, 27, 5, 5, 5, 5, 5

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OFFSET

1,1

COMMENTS

A391583 gives the corresponding m.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

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) * n = A048720(a(n), A391583(n)).

a(2*n) = a(n).

PROG

(PARI)

A048720(b, c) = fromdigits(Vec(Pol(binary(b))*Pol(binary(c)))%2, 2);

A391582(n) = { my(th=2); forstep(k=3, oo, 2, my(Pnk=Pol(binary(n*k))*Mod(1, 2), Pk=Pol(binary(k))*Mod(1, 2)); if(0==lift(Pnk % Pk), if(th>1, th--, return(k)))); };

CROSSREFS

Cf. A048720, A391583.

Column 3 of A391725 (cf. also A391570, which is column 2).

Sequence in context: A076568 A139259 A105444 * A240233 A033299 A293982

Adjacent sequences: A391579 A391580 A391581 * A391583 A391584 A391585

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Dec 18 2025

STATUS

approved