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A194606 Least k >= 0 such that prime(n)*2^k - 1 or prime(n)*2^k + 1 is prime, or -1 if no such value exists, where prime(n) denotes the n-th prime number.

%I A194606 #22 Feb 16 2025 08:33:15
%S A194606 0,0,1,1,1,2,2,1,1,1,1,1,1,2,4,1,5,3,2,2,2,1,1,1,1,3,3,3,6,1,2,1,2,1,
%T A194606 3,4,1,2,4,1,1,3,1,2,2,1,1,3,2,1,1,1,11,1,4,2,3,1,2,1,11,1,1,9,3,6,1,
%U A194606 1,3,3,4,1,1,2,1,2,11,4,3,2,1,4,1,2,1,1
%N A194606 Least k >= 0 such that prime(n)*2^k - 1 or prime(n)*2^k + 1 is prime, or -1 if no such value exists, where prime(n) denotes the n-th prime number.
%C A194606 A194607 gives the record values.
%H A194606 Arkadiusz Wesolowski, <a href="/A194606/b194606.txt">Table of n, a(n) for n = 1..1000</a>
%H A194606 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BrierNumber.html">Brier Number</a>
%e A194606 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)=1.
%t A194606 Table[p = Prime[n]; k = 0; While[! PrimeQ[p*2^k - 1] && ! PrimeQ[p*2^k + 1], k++]; k, {n, 100}] (* _Arkadiusz Wesolowski_, Sep 04 2011 *)
%Y A194606 Cf. A194591, A194600, A194603, A194607, A194608, A194635, A194636, A194637, A194638, A194639.
%Y A194606 Cf. A040081, A040076, A076335, A180247.
%K A194606 sign
%O A194606 1,6
%A A194606 _Arkadiusz Wesolowski_, Aug 30 2011