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.
5, 7, 9, 11, 13, 17, 19, 21, 23, 25, 29, 31, 35, 37, 39, 41, 43, 47, 49, 51, 53, 55, 59, 61, 65, 67, 69, 71, 73, 77, 79, 81, 83, 85, 89, 91, 95, 97, 99, 101, 103, 107, 109, 111, 113, 115, 119, 121
Offset: 1
Examples
3 is not in the sequence because 3*4^1 - 1 = 11 and 3*4^1 + 1 = 13 are a pair of twin primes. 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.
Crossrefs
Cf. A237592.
Programs
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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;
Comments