A247138 Least k >= 0 such that 2n+1 - 2^k is a prime power, or -1 if no such k exists.

-1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 3, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 0, 3, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 3, 1, 2, 4, 3, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 3, 1, 2, 1, 0, 2, 1, 2, 4, 1, 1, 2, 3, 3, -1, 1, 1, 2, 3, 1, 2, 5, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 2, 3, 3, 6, 1, 1, 2, 1, 1, 2, 3, 3, 4, 5, 1, 2, 7, 3, 6, 5, 1, 2, 1, 1, 2, 1, 2, 4, 1, 1, 1, 2, 3, 3, 1, 2, 0, 1, 2

Offset

0,12

Comments

It seems to make no difference whether one requires a prime power > 1 or a prime power including 1.

While such k >= 0 exists for most odd numbers 2n+1, there are only very few even numbers of this form.

Links

Table of n, a(n) for n=0..130.

Prog

(PARI) a(n)=for(k=0, log(n=n*2+1)\log(2)+1, (/*n-2^k==1 ||*/ isprimepower(n-2^k))&&return(k)); -1

Crossrefs

Cf. A000079, A000961.

Sequence in context: A059883 A086967 A098490 * A212627 A029419 A165105

Adjacent sequences: A247135 A247136 A247137 * A247139 A247140 A247141

Keyword

sign

Author

M. F. Hasler, Nov 20 2014

Status

approved