A194608 Smallest prime either of the form prime(n)*2^k - 1 or prime(n)*2^k + 1, k >= 0, or 0 if no such prime exists, where prime(n) denotes the n-th prime number.

3, 2, 11, 13, 23, 53, 67, 37, 47, 59, 61, 73, 83, 173, 751, 107, 1889, 487, 269, 283, 293, 157, 167, 179, 193, 809, 823, 857, 6977, 227, 509, 263, 547, 277, 1193, 2417, 313, 653, 2671, 347, 359, 1447, 383, 773, 787, 397, 421, 1783, 907, 457, 467, 479, 493567

Offset: 1

Author

Arkadiusz Wesolowski, Aug 30 2011

Keywords

• nonn

Comments

Primes arising from A194606 (or 0 if no such prime exists).

Examples

			For n=4, 7*2^0-1 and 7*2^0+1 are composite, but 7*2^1-1=13 is prime, so a(4)=13.
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A194591, A194600, A194603, A194606, A194607, A194635, A194636, A194637, A194638, A194639.

Cf. A038699, A050921, A076335, A180247.

Programs

Mathematica

Table[p = Prime[n]; k = 0; While[! PrimeQ[a = p*2^k - 1] && ! PrimeQ[a = p*2^k + 1], k++]; a, {n, 100}] (* Arkadiusz Wesolowski, Sep 04 2011 *)