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A194636 Least k >= 0 such that (2*n-1)*2^k - 1 or (2*n-1)*2^k + 1 is prime, or -1 if no such value exists.

%I A194636 #21 Feb 16 2025 08:33:15
%S A194636 0,0,1,1,1,1,2,1,2,1,1,1,2,1,1,1,1,1,1,1,1,2,1,4,1,1,1,1,1,5,3,1,1,2,
%T A194636 1,2,2,1,2,1,1,1,4,1,1,1,2,1,1,1,3,3,1,3,6,1,1,1,1,1,1,2,1,2,1,1,3,1,
%U A194636 2,1,1,2,5,1,3,4,1,1,1,1,2,2,1,4,1,2
%N A194636 Least k >= 0 such that (2*n-1)*2^k - 1 or (2*n-1)*2^k + 1 is prime, or -1 if no such value exists.
%C A194636 Bisection of A194591: a(n) = A194591(2*n-1).
%C A194636 A194637 gives the record values.
%H A194636 Arkadiusz Wesolowski, <a href="/A194636/b194636.txt">Table of n, a(n) for n = 1..1000</a>
%H A194636 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BrierNumber.html">Brier Number</a>
%e A194636 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 A194636 Table[n = 2*n - 1; k = 0; While[! PrimeQ[n*2^k - 1] && ! PrimeQ[n*2^k + 1], k++]; k, {n, 100}] (* _Arkadiusz Wesolowski_, Sep 04 2011 *)
%t A194636 p[n_]:=Module[{c=2n-1,k=0},While[!Or@@PrimeQ[c*2^k+{1,-1}],k++];k]; Array[ p,90] (* _Harvey P. Dale_, Mar 08 2013 *)
%Y A194636 Cf. A194591, A194600, A194603, A194606, A194607, A194608, A194635, A194637, A194638, A194639.
%Y A194636 Cf. A040081, A040076, A076335, A180247.
%K A194636 sign
%O A194636 1,7
%A A194636 _Arkadiusz Wesolowski_, Aug 31 2011