|
| |
|
|
A040076
|
|
Smallest m >= 0 such that n*2^m+1 is prime, or -1 if no such m exists.
|
|
16
| |
|
|
0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 3, 0, 6, 1, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 8, 3, 1, 2, 1, 0, 2, 5, 1, 0, 1, 0, 2, 1, 2, 0, 583, 1, 2, 1, 1, 0, 1, 1, 4, 1, 2, 0, 5, 0, 4, 7, 1, 2, 1, 0, 2, 1, 1, 0, 3, 0, 2, 1, 1, 4, 3, 0, 2, 3, 1, 0, 1, 2, 4, 1, 2, 0, 1, 1, 8, 7, 2, 582, 1, 0, 2, 1, 1, 0, 3, 0
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,7
|
|
|
COMMENTS
| Sierpinski showed that a(n) = -1 infinitely often. John Selfridge showed that a(78557) = -1 and it is conjectured that a(n) >= 0 for all n < 78557.
|
|
|
LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000 (with help from the Sierpinski problem website)
Ray Ballinger and Wilfrid Keller, The Sierpinski Problem: Definition and Status
Seventeen or Bust, A Distributed Attack on the Sierpinski problem
|
|
|
EXAMPLE
| 1*(2^0)+1=2 is prime, so a(1)=0;
3*(2^1)+1=5 is prime, so a(3)=1;
For n=7, 7+1 and 7*2+1 are composite, but 7*2^2+1=29 is prime, so a(7)=2.
|
|
|
MATHEMATICA
| Do[m = 0; While[ !PrimeQ[n*2^m + 1], m++ ]; Print[m], {n, 1, 110} ]
|
|
|
CROSSREFS
| For the corresponding primes see A050921.
Cf. A103964, A040081.
Cf. A033809, A046067 (odd n), A057192 (prime n)
Sequence in context: A130538 A078659 A079690 * A019269 A204459 A035155
Adjacent sequences: A040073 A040074 A040075 * A040077 A040078 A040079
|
|
|
KEYWORD
| easy,nice,sign
|
|
|
AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
|
| |
|
|
