login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A040076 Smallest m >= 0 such that n*2^m+1 is prime, or -1 if no such m exists. 20
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; text; internal format)
OFFSET

1,7

COMMENTS

Sierpiński 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.

Determining a(131072) = a(2^17) is equivalent to finding the next Fermat prime after F_4 = 2^16 + 1. - Jeppe Stig Nielsen, Jul 27 2019

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000 (with help from the Sierpiński problem website)

Ray Ballinger and Wilfrid Keller, The Sierpiński Problem: Definition and Status

Seventeen or Bust, A Distributed Attack on the Sierpiński 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: A257510 A305445 A225721 * A019269 A204459 A035155

Adjacent sequences:  A040073 A040074 A040075 * A040077 A040078 A040079

KEYWORD

easy,nice,sign

AUTHOR

David W. Wilson

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)