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%I #11 Sep 08 2022 08:46:18
%S 5,7,9,11,13,17,19,21,23,25,29,31,35,37,39,41,43,47,49,51,53,55,59,61,
%T 65,67,69,71,73,77,79,81,83,85,89,91,95,97,99,101,103,107,109,111,113,
%U 115,119,121
%N Odd numbers n such that for all k >= 1 the numbers n*4^k - 1 and n*4^k + 1 do not form a twin prime pair.
%C Next term is 123 or 125.
%C A sufficient condition for an odd number > 1 to belong to this sequence is that it not be congruent to 3, 15 or 27 mod 30.
%e 3 is not in the sequence because 3*4^1 - 1 = 11 and 3*4^1 + 1 = 13 are a pair of twin primes.
%e 5 is in the sequence because gcd(5 + 1, 4 - 1) = 3 is a trivial factor of 5*4^k + 1. Therefore, for all k >= 1 the numbers 5*4^k - 1 and 5*4^k + 1 do not form a twin prime pair.
%o (Magma) lst:=[]; for n in [3..121 by 2] do if not n mod 30 in {3, 15, 27} then Append(~lst, n); else k:=1; while not IsPrime(n*4^k+1) or not IsPrime(n*4^k-1) do k+:=1; end while; end if; end for; lst;
%Y Cf. A237592.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Feb 05 2017