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
Keywords
Examples
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).
Links
- Pierre CAMI, Table of n, a(n) for n = 1..1800
Programs
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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 *) -
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