A204988 The index j < k such that n divides 2^k - 2^j, where k is the least index (A204987) for which such j exists.

1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 4, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 5, 1, 1, 1, 2, 1, 1, 1, 3, 1

Offset: 1

Author

Clark Kimberling, Jan 21 2012

Keywords

• nonn
• mult

Comments

For a guide to related sequences, see A204892.

Examples

			(See example at A204987.)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..6556

Crossrefs

Cf. A007814, A204892, A204987.

Programs

Mathematica

(See the program at A204987.)
a[n_] := Max[1, IntegerExponent[n, 2]]; Array[a, 100] (* Amiram Eldar, Oct 22 2022 *)

PARI

\\ Use the program at A204987. - Antti Karttunen, Nov 19 2017

PARI

a(n)=max(1, valuation(n,2)); \\ Andrew Howroyd, Aug 08 2018

Formula

a(n) = A007814(n) + (1-(-1)^n)/2 (conjecture). - Velin Yanev, Nov 14 2016.

From Andrew Howroyd, Aug 08 2018: (Start)

The above conjecture is true because the definition of this sequence and A204987 requires j to be at least 1 and 2^k - 2^j can be written 2^j*(2^(k-j) - 1).

a(n) = max(1, A007814(n)). (End)

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3/2. - Amiram Eldar, Oct 22 2022

Extensions

More terms from Antti Karttunen, Nov 19 2017

Keyword:mult added by Andrew Howroyd, Aug 08 2018