This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A253719 #16 May 03 2015 17:54:06 %S A253719 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, %T A253719 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, %U A253719 2,2,2,2,4,2,3,4,4,4,2,4,4,6,2,2,5,8,4 %N A253719 Least k>0 such that n AND (n^k) <= 1, where AND denotes the bitwise AND operator. %C A253719 This sequence is well defined: for any n such that n < 2^m: %C A253719 - If n is even, then n^m = 0 mod 2^m, hence n AND (n^m) = 0, and a(n) <= m, %C A253719 - 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). %C A253719 a(2*(2^m-1)) = m+1 for any m>=0. - _Paul Tek_, May 03 2015 %H A253719 Paul Tek, <a href="/A253719/b253719.txt">Table of n, a(n) for n = 0..100000</a> %e A253719 11 AND (11^1) = 11, %e A253719 11 AND (11^2) = 9, %e A253719 11 AND (11^3) = 3, %e A253719 11 AND (11^4) = 1, %e A253719 hence a(11)=4. %o A253719 (PARI) a(n) = my(k=1, nk=n); while (bitand(n, nk)>1, k=k+1; nk=nk*n); return (k) %Y A253719 Cf. A224694. %K A253719 nonn,base %O A253719 0,3 %A A253719 _Paul Tek_, May 02 2015