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Indices of records in A194591 restricted to prime indices.
13

%I #37 Aug 12 2023 05:16:01

%S 2,5,13,47,59,109,241,631,1109,1373,1447,16229,52267,56543,838441,

%T 16935761,270704167,3296757029

%N Indices of records in A194591 restricted to prime indices.

%C 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.

%C a(19) > 10^10.

%C A194607 gives the record values of A194606.

%D Wilfrid Keller, personal communication, 2010.

%H Chris K. Caldwell, The List of Largest Known Primes, <a href="https://t5k.org/primes/page.php?id=6614">270704167 * 2^85461 - 1</a>

%H Chris K. Caldwell, The List of Largest Known Primes, <a href="https://t5k.org/primes/page.php?id=596">3296757029 * 2^191207 + 1</a>

%H Carlos Rivera, <a href="http://www.primepuzzles.net/problems/prob_030.htm">Problem 30. A stepladder to B-alpha sequence</a>, The Prime Puzzles & Problems Connection.

%t 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 *)

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

%Y Cf. A064699, A076335, A180247, A217892.

%K more,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 31 2011

%E a(17) was found in 2000 by Wilfrid Keller

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

%E Edited by _Max Alekseyev_, Oct 14 2012

%E Edited by _Arkadiusz Wesolowski_, Sep 11 2013