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

1,1

Comments

Next term is 123 or 125.

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.

Links

Table of n, a(n) for n=1..48.

Example

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.

Prog

(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;

Crossrefs

Cf. A237592.

Sequence in context: A230203 A339910 A303578 * A336366 A088502 A081001

Adjacent sequences: A282054 A282055 A282056 * A282058 A282059 A282060

Keyword

nonn

Author

Arkadiusz Wesolowski, Feb 05 2017

Status

approved