This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A282057 #14 Feb 10 2025 03:12:19
%S A282057 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 A282057 65,67,69,71,73,77,79,81,83,85,89,91,95,97,99,101,103,107,109,111,113,
%U A282057 115,119,121
%N A282057 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 A282057 Next term is 123 or 125.
%C A282057 A sufficient condition for an odd number > 1 to belong to this sequence is that it is not congruent to 3, 15 or 27 mod 30.
%e A282057 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 A282057 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 A282057 (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 A282057 Cf. A237592.
%K A282057 nonn,more
%O A282057 1,1
%A A282057 _Arkadiusz Wesolowski_, Feb 05 2017