A178253 - OEIS

A178253

a(n) is the least positive integer m such that (A001969(n))^m is in A000069.

4, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 5, 2, 4, 2, 2, 2, 2, 2, 2, 3, 2, 4, 2, 4, 5, 5, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 4, 3, 2, 2, 5, 4, 5, 3, 2, 5, 2, 3, 4, 3, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 3, 4, 2, 2, 2, 2, 4, 2, 3, 3, 2, 3, 2, 2, 4, 3, 2, 3, 2, 2, 2, 3, 2, 5

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OFFSET

2,1

COMMENTS

Conjecture: a(n) exists for all n >= 2.

The values of A001969(n)^m are given in A178373. [From Jeremy Gardiner, May 26 2010]

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 2..10000

FORMULA

If k=A001969(n)=2^m*A001969(s), where A001969(s) is odd, then a(n)=a(s).

PROG

(PARI) a(n)=my(e=2*n--+hammingweight(n)%2, m=1); e>>=valuation(e, 2); while(hammingweight(e^m++)%2==0, ); m \\ Charles R Greathouse IV, Mar 22 2013