A320386 a(n) is the smallest positive integer such that the binary representation of n*a(n) is a "binary square" (i.e., a term of A020330).

3, 5, 1, 9, 2, 6, 9, 17, 4, 1, 17, 3, 17, 17, 1, 33, 8, 2, 33, 33, 3, 24, 33, 22, 33, 33, 2, 33, 33, 22, 33, 65, 16, 4, 65, 1, 65, 65, 22, 52, 65, 22, 65, 12, 1, 65, 65, 11, 65, 52, 3, 40, 65, 1, 12, 65, 11, 65, 65, 11, 65, 65, 1, 129, 32, 8, 129, 2, 11, 39

Offset

1,1

Comments

a(n) exists because if n has t bits, then (2^t+1)*n is a binary square.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..8191

Example

a(5) = 2 because 5 is not a binary square, but 5*2 = 10 is (its binary representation is 1010).

Maple

a:= proc(n) local k; for k while not (s-> (l->
      l::even and s[1..l/2]=s[l/2+1..l])(length(s)))(
      convert(convert(k*n, binary), string)) do od; k
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Oct 12 2018

Prog

(PARI) is(n) = my(L=#binary(n)\2); n>>L==bitand(n, 2^L-1); \\ A020330
a(n) = my(k=1); while (!is(k*n), k++); k; \\ Michel Marcus, Oct 12 2018

Crossrefs

Cf. A020330.

Sequence in context: A212695 A209422 A361944 * A112411 A283838 A228146

Adjacent sequences: A320383 A320384 A320385 * A320387 A320388 A320389

Keyword

nonn,base

Author

Jeffrey Shallit, Oct 12 2018

Status

approved