A135434 -id:A135434 - cp's OEIS frontend

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

Pierre CAMI, Dec 26 2014

			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.

Cf. A000043, A135434.

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 *)

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

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

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

A249806 Smallest odd number k>1 such that k*2^prime(n)-1 is also prime.

Original entry on oeis.org

3, 3, 7, 3, 3, 9, 7, 51, 13, 7, 15, 21, 15, 3, 31, 147, 45, 69, 43, 73, 15, 69, 91, 19, 51, 81, 3, 25, 9, 85, 103, 55, 169, 225, 109, 145, 15, 103, 615, 69, 259, 69, 63, 45, 285, 471, 9, 255, 169, 489, 69, 273, 427, 43, 391, 169, 201, 21

Offset: 1

Pierre CAMI, Nov 06 2014

nonn

If prime(n) is a Mersenne prime exponent then 2^prime(n)-1 is a prime < k*2^prime(n)-1.

Pierre CAMI, Table of n, a(n) for n = 1..1000

Cf. A135434.

3*2^2-1=11 prime so a(1)=3.
3*2^3-1=23 prime so a(2)=3.
3*2^5-1=95 composite, 5*2^5-1=159 composite, 7*2^5-1=223 prime so a(3)=7.

a249806[n_Integer] := Catch[Module[{k}, For[k = 3, k < 10^5, k += 2, If[PrimeQ[k*2^Prime[n] - 1], Throw[k], 0]]]]; a249806 /@ Range[120] (* Michael De Vlieger, Nov 11 2014 *)

s=[]; forprime(p=2, 500, k=3; q=2^p; while(!ispseudoprime(k*q-1), k+=2); s=concat(s, k)); s \\ Colin Barker, Nov 06 2014

cp's OEIS Frontend

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

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