A249382 Smallest odd prime Q such that Q*2^prime(n)-1 is also a prime number.

3, 3, 7, 3, 3, 31, 7, 61, 13, 7, 43, 31, 19, 3, 31, 307, 733, 79, 43, 73, 421, 73, 181, 19, 157, 181, 3, 739, 421, 127, 103, 73, 571, 421, 109, 211, 1459, 103, 1693, 487, 829, 139, 1153, 439, 3067, 601, 199, 853, 421, 3541, 1069, 1279, 1297

Offset

1,1

Links

Pierre CAMI, Table of n, a(n) for n = 1..1800

Example

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

Mathematica

a249382[n_Integer] := Module[{q = 2}, While[! PrimeQ[Prime[q]*2^Prime[n] - 1], q++]; Prime[q]]; a249382/@Range[53] (* Michael De Vlieger, Nov 12 2014 *)

Prog

(PFGW & SCRIPT)
SCRIPT
DIM i
DIM j
DIM n, 0
OPENFILEOUT myf, a(n)
LABEL loop1
SET n, n+1
SET i, 1
LABEL loop2
SET i, i+1
SET j, p(i)
PRP j*2^p(n)-1
IF ISPRP THEN GOTO a
GOTO loop2
LABEL a
WRITE myf, j
GOTO loop1
(PARI) listp(nn) = {for (n=1, nn, k=2; while(!isprime(prime(k)*2^prime(n)-1), k++); print1(prime(k), ", "); ); } \\ Michel Marcus, Oct 27 2014

Crossrefs

Cf. A249383, A249384.

Sequence in context: A359048 A096915 A249806 * A317929 A285387 A100803

Adjacent sequences: A249379 A249380 A249381 * A249383 A249384 A249385

Keyword

nonn

Author

Pierre CAMI, Oct 27 2014

Status

approved