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A320386 a(n) is the smallest positive integer such that the binary representation of n*a(n) is a "binary square" (i.e., a member of A020330). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A235605 A212695 A209422 * A112411 A283838 A228146

Adjacent sequences:  A320383 A320384 A320385 * A320387 A320388 A320389

KEYWORD

nonn,base

AUTHOR

Jeffrey Shallit, Oct 12 2018

STATUS

approved

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Last modified September 29 20:22 EDT 2020. Contains 337432 sequences. (Running on oeis4.)