The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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