A194635 Indices of records in A194591 restricted to prime indices.

2, 5, 13, 47, 59, 109, 241, 631, 1109, 1373, 1447, 16229, 52267, 56543, 838441, 16935761, 270704167, 3296757029

Offset: 1

Author

Arkadiusz Wesolowski, Aug 31 2011

Keywords

• more
• nonn

Comments

Integers for which the smallest k in A194591 such that prime(n)*2^k - 1 or prime(n)*2^k + 1 is prime (A194608) increases.

a(19) > 10^10.

A194607 gives the record values of A194606.

References

• Wilfrid Keller, personal communication, 2010.

Links

• Chris K. Caldwell, The List of Largest Known Primes, 270704167 * 2^85461 - 1
• Chris K. Caldwell, The List of Largest Known Primes, 3296757029 * 2^191207 + 1
• Carlos Rivera, Problem 30. A stepladder to B-alpha sequence, The Prime Puzzles & Problems Connection.

Crossrefs

Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194636, A194637, A194638, A194639.

Cf. A064699, A076335, A180247, A217892.

Programs

Mathematica

l = -1; Flatten[Table[p = Prime[n]; k = 0; While[! PrimeQ[p*2^k - 1] && ! PrimeQ[p*2^k + 1], k++]; If[k > l, l = k; p, {}], {n, 10^4}]] (* Arkadiusz Wesolowski, Sep 04 2011 *)

Extensions

a(17) was found in 2000 by Wilfrid Keller

a(18) was found in 2003 by Patrick De Geest

Edited by Max Alekseyev, Oct 14 2012

Edited by Arkadiusz Wesolowski, Sep 11 2013