A253242 Least k>=0 such that n^(2^k)+1 is prime (for even n), or (n^(2^k)+1)/2 is prime (for odd n); -1 if no such k exists.
0, 0, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, -1, 0, 1, 0
Offset: 2
Examples
a(7) = 2 since (7^(2^0)+1)/2 and (7^(2^1)+1)/2 are not primes, but (7^(2^2)+1)/2 = 1201 is prime. a(14) = 1 since 14^(2^0)+1 is not prime, but 14^(2^1)+1 = 197 is prime.
Links
- Eric Chen, Table of n, a(n) for n = 2..1500 status (for the -1s, only a(n) for n in A070265 are proved, all other -1s are only conjectured)
- Gary Barnes, List of generalized Fermat primes in even bases up to 1030
- Eric Chen, List of generalized Fermat primes in bases up to 1000
- Chris Caldwell, Generalized Fermat number
- Richard Fischer, List of generalized Fermat primes in odd bases
- Yves Gallot, Generalized Fermat prime search
- Wilfrid Keller, Factorization of GFN(n,2)
- Wilfrid Keller, Factorization of GFN(n,3)
- Wilfrid Keller, Factorization of GFN(n,5)
- Wilfrid Keller, Factorization of GFN(n,6)
- Wilfrid Keller, Factorization of GFN(n,10)
- Wilfrid Keller, Factorization of GFN(n,12)
- Jeppe Stig Salling Nielsen, List of generalized Fermat primes in even bases up to 1000
- MathWorld, Generalized Fermat number
- OEIS wiki, Generalized Fermat number
- Wikipedia, Generalized Fermat number
Crossrefs
Programs
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Mathematica
Table[k=0; While[p=If[EvenQ[n], (2n)^(2^k)+1, ((2n)^(2^k)+1)/2]; k<12 && !PrimeQ[p], k=k+1]; If[k==12, -1, k], {n, 2, 1500}] -
PARI
f(n) = for(k=0, 11, if(ispseudoprime(n^(2^k)+1), return(k))); -1 g(n) = for(k=0, 11, if(ispseudoprime((n^(2^k)+1)/2), return(k))); -1 a(n) = if(n%2==0, f(n), g(n))
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PARI
f(n,k)=if(n%2, (n^(2^k)+1)/2, n^(2^k)+1) a(n)=if(ispower(-n), -1, my(k); while(!ispseudoprime(f(n,k)), k++); k) \\ Charles R Greathouse IV, Apr 20 2015
Comments