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A318569 a(n) is the smallest positive integer such that n*a(n) is a "binary antipalindrome" (i.e., an element of A035928). 0
2, 1, 4, 3, 2, 2, 6, 7, 62, 1, 62, 1, 4, 3, 10, 15, 10, 31, 2, 12, 2, 31, 26, 10, 6, 2, 116, 2, 8, 5, 18, 31, 254, 5, 78, 26, 18, 1, 24, 6, 18, 1, 70, 86, 11894, 13, 254, 5, 46, 3, 4, 1, 4, 58, 264, 1, 850, 4, 162, 4, 16, 9, 34, 63, 38, 127, 56, 3, 42, 39, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) exists:  write n = r*2^i, where r is odd.  Then r divides 2^phi(r) - 1, where phi is the Euler phi function.  Choose k such that k phi(r) >= i.

Then n divides (2^{k*phi(r)} - 1)*2^{k*phi(r)}, which is a binary antipalindrome.

LINKS

Table of n, a(n) for n=1..71.

CROSSREFS

Cf. A035928.

Sequence in context: A302436 A283167 A080079 * A277749 A227629 A183201

Adjacent sequences:  A318566 A318567 A318568 * A318570 A318571 A318572

KEYWORD

nonn,base

AUTHOR

Jeffrey Shallit, Oct 12 2018

STATUS

approved

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Last modified December 7 09:33 EST 2019. Contains 329843 sequences. (Running on oeis4.)