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

1,1

Links

Table of n, a(n) for n=1..35.

Example

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.

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 *)

Prog

(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
(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

Crossrefs

Cf. A000043, A135434.

Sequence in context: A020765 A112756 A121795 * A249384 A228446 A364564

Adjacent sequences: A253024 A253025 A253026 * A253028 A253029 A253030

Keyword

nonn,more

Author

Pierre CAMI, Dec 26 2014

Extensions

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

Status

approved