A195986 Exponent of the largest power of 2 that divides 5^n - 3^n.

1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 7, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 8, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 7, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 9, 1, 4, 1, 5, 1, 4, 1, 6, 1, 4, 1, 5, 1, 4, 1, 7, 1, 4, 1, 5, 1, 4

Offset: 1

Author

John W. Layman, Oct 12 2011

Keywords

• nonn

Comments

Conjecture: a(n) = 1 if A090740 = 1, else a(n) = A090740(n)+1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383

Crossrefs

Cf. A005058, A007814, A090740.

Programs

Mathematica

Table[IntegerExponent[5^n - 3^n, 2], {n, 100}] (* T. D. Noe, Oct 12 2011 *)

PARI

A195986(n) = valuation(5^n - 3^n,2); \\ Antti Karttunen, Nov 06 2018

Formula

a(n) = A007814(A005058(n)). - Antti Karttunen, Nov 06 2018

Extensions

Name clarified by Antti Karttunen, Nov 06 2018