A253027 Smallest odd number k>1 such that k*2^A000043(n)+1 is a prime number.

3, 5, 3, 5, 5, 9, 11, 35, 53, 51, 105, 5, 233, 347, 125, 369, 2063, 89, 4715, 1145, 885, 4839, 2711, 30611, 5859, 2543, 21509, 114071, 309, 60191, 524489, 33305, 306363, 987537, 509765

Offset: 1

Author

Pierre CAMI, Dec 26 2014

Keywords

• nonn
• more

Examples

			3*2^2+1=13 prime so a(1)=3 as A000043(1)=2.
3*2^3+1=25 composite, 5*2^3+1=41 prime so a(2)=5 as A000043(2)=3.
3*2^5+1=97 prime so a(3)=3 as A000043(3)=5.
		

Crossrefs

Cf. A000043, A135434.

Programs

Mathematica

a253027[n_] :=
Block[{k, t = Select[Prime[Range[n]], PrimeQ[2^# - 1] &], l},
  l = Length[t];
Table[k = 3; While[! PrimeQ[k*2^t[[i]] + 1], k = k + 2]; k, {i, l}]]; a253027[600] (* Michael De Vlieger, Dec 26 2014 *)

PARI

lista(nn) = {forprime (n=1, nn, if (isprime(2^n-1), k=3; while (!isprime(k*2^n+1), k += 2); print1(k, ", ");););} \\ Michel Marcus, Dec 27 2014

PFGW

Command pfgw64 -f -e1000000 in.txt
in.txt file :
ABC2 a$*2^756839+$b // {number_primes,$b,1}
b: from 1 to 1
a: from 1 to 1000000

Extensions

a(33)-a(35) from Pierre CAMI, Apr 06 2015