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A247134 Least k such that 2n+1 = 2^k - p^m for some prime p and integer m > 0, or 0 if no such k exists. 1
2, 3, 3, 4, 4, 4, 4, 5, 6, 5, 5, 5, 5, 5, 5, 7, 6, 6, 6, 6, 6, 29, 6, 6, 7, 6, 6, 6, 6, 6, 6, 8, 8, 7, 7, 10, 9, 7, 8, 7, 7, 8, 7, 7, 8, 7, 8, 10, 7, 7, 7, 7, 7, 8, 7, 7, 10, 7, 7, 7, 7, 7, 7, 47, 8, 8, 9, 8, 10, 9, 10, 8, 9, 8, 8, 9, 8, 8, 15, 8, 10, 9, 9, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Since even numbers cannot be of this form unless they are powers of 2, only odd 2n+1 are considered.
Except for n=3, 11, 18, 19, 27, 39, 50, 51, ..., the value of k corresponds to m=1, i.e., 2^k - (2n+1) is prime.
a(935) >= 70000. - Hiroaki Yamanouchi, Nov 22 2014
LINKS
FORMULA
a(n) = min{ k | exists m>1: 2n+1 = A000079(k) - A000961(m) } > log_2(n).
PROG
(PARI) a(n)=for(k=log(n=n*2+1)\log(2)+1, 9e9, isprimepower(2^k-n)&&return(k))
CROSSREFS
Sequence in context: A061775 A356384 A225634 * A080604 A357815 A221983
KEYWORD
nonn
AUTHOR
M. F. Hasler, Nov 20 2014
STATUS
approved

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Last modified March 28 07:18 EDT 2024. Contains 371235 sequences. (Running on oeis4.)