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A253719 Least k>0 such that n AND (n^k) <= 1, where AND denotes the bitwise AND operator. 2
1, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 4, 2, 4, 4, 2, 2, 2, 2, 2, 3, 6, 5, 4, 2, 4, 2, 8, 3, 8, 5, 2, 2, 2, 2, 2, 2, 2, 3, 6, 2, 2, 4, 12, 2, 4, 4, 4, 2, 4, 2, 10, 3, 14, 6, 8, 2, 8, 6, 16, 3, 16, 6, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 4, 4, 4, 2, 4, 4, 6, 2, 2, 5, 8, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence is well defined: for any n such that n < 2^m:

- If n is even, then n^m = 0 mod 2^m, hence n AND (n^m) = 0, and a(n) <= m,

- If n is odd, then n^phi(2^m) = 1 mod 2^m according to Euler's totient theorem, hence n AND (n^phi(2^m)) = 1, and a(n) <= phi(2^m).

a(2*(2^m-1)) = m+1 for any m>=0. - Paul Tek, May 03 2015

LINKS

Paul Tek, Table of n, a(n) for n = 0..100000

EXAMPLE

11 AND (11^1) = 11,

11 AND (11^2) = 9,

11 AND (11^3) = 3,

11 AND (11^4) = 1,

hence a(11)=4.

PROG

(PARI) a(n) = my(k=1, nk=n); while (bitand(n, nk)>1, k=k+1; nk=nk*n); return (k)

CROSSREFS

Cf. A224694.

Sequence in context: A217619 A187186 A259651 * A081147 A236103 A278293

Adjacent sequences:  A253716 A253717 A253718 * A253720 A253721 A253722

KEYWORD

nonn,base

AUTHOR

Paul Tek, May 02 2015

STATUS

approved

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Last modified April 21 10:28 EDT 2021. Contains 343149 sequences. (Running on oeis4.)