|
| |
|
|
A057192
|
|
Least m such that 1+prime(n)*2^m is a prime, or -1 if no such m exists.
|
|
8
| |
|
|
0, 1, 1, 2, 1, 2, 3, 6, 1, 1, 8, 2, 1, 2, 583, 1, 5, 4, 2, 3, 2, 2, 1, 1, 2, 3, 16, 3, 6, 1, 2, 1, 3, 2, 3, 4, 8, 2, 7, 1, 1, 4, 1, 2, 15, 2, 20, 8, 11, 6, 1, 1, 36, 1, 279, 29, 3, 4, 2, 1, 30, 1, 2, 9, 4, 7, 4, 4, 3, 10, 21, 1, 12, 2, 14, 6393, 11, 4, 3, 2, 1, 4, 1, 2, 6, 1, 3, 8, 5, 6, 19, 3, 2, 1, 2, 5
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
COMMENTS
| Primes p such that p*2^m+1 is composite for all m are called Sierpinski numbers. The smallest known prime Sierpinski number is 271129. Currently, 10223 is the smallest prime whose status is unknown.
For 0 < k < a(n), prime(n)*2^k is a nontotient. See A005277. - T. D. Noe, Sep 13 2007
|
|
|
REFERENCES
| See A046067
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Ray Ballinger and Wilfrid Keller, Sierpinski Problem
Seventeen or Bust, A Distributed Attack on the Sierpinski problem
|
|
|
EXAMPLE
| a(8)=6 because prime(8)=19 and the first prime in the sequence 1+19*{2,4,8,16,32,64}={39,77,153,305,609,1217} is 1217=1+19*2^6.
|
|
|
MATHEMATICA
| Table[p=Prime[n]; k=0; While[ ! PrimeQ[1+p*2^k], k++ ]; k, {n, 100}] (Noe)
|
|
|
CROSSREFS
| Cf. A058887, A058811, A058812, A002202, A014197, A005277, A005384, A005385, A051686.
Cf. A046067 (least k such that (2n-1)*2^k+1 is prime).
Sequence in context: A125596 A204994 A132405 * A078777 A135938 A079210
Adjacent sequences: A057189 A057190 A057191 * A057193 A057194 A057195
|
|
|
KEYWORD
| sign
|
|
|
AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jan 10 2001
|
|
|
EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Aug 03 2005
|
| |
|
|
