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

Offset: 2

Author

Vladimir Shevelev, May 24 2010, May 25 2010

Keywords

• nonn
• easy

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

Crossrefs

Cf. A000069, A001969, A178373.

Programs

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

Formula

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

Extensions

Extended by Jeremy Gardiner, May 26 2010

Edited by N. J. A. Sloane, Jun 08 2010