A224694 -id:A224694 - cp's OEIS frontend

A253719 Least k>0 such that n AND (n^k) <= 1, where AND denotes the bitwise AND operator.

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

Offset: 0

Paul Tek, May 02 2015

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

			11 AND (11^1) = 11,
11 AND (11^2) = 9,
11 AND (11^3) = 3,
11 AND (11^4) = 1,
hence a(11)=4.

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

Cf. A224694.

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

A366201 Number x such that triangular(x) AND x^2 = 0, where AND is the bitwise logical-and operation.

Original entry on oeis.org

0, 2, 3, 4, 8, 12, 16, 18, 24, 32, 34, 46, 48, 52, 64, 66, 68, 94, 96, 128, 130, 132, 144, 188, 192, 208, 256, 258, 260, 264, 288, 384, 415, 416, 512, 514, 516, 520, 544, 551, 576, 736, 768, 816, 831, 832, 1024, 1026, 1028, 1032, 1040, 1042, 1088, 1090, 1152, 1163

Offset: 1

Alex Ratushnyak, Oct 04 2023

Numbers x such that A000217(x) AND A000290(x) = 0.

Cf. A000217, A000290, A004198 (AND).

Cf. A224694.

cp's OEIS Frontend

A253719 Least k>0 such that n AND (n^k) <= 1, where AND denotes the bitwise AND operator.

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