A274001 Even numbers with a unique resolution as the sum of two primes, each of which has a twin.

6, 8, 12, 28, 40, 52, 56, 68, 124, 128, 136, 172, 176, 188, 226, 262, 266, 304, 308, 394, 396, 398, 412, 416, 442, 446, 484, 488, 544, 548, 556, 560, 608, 634, 638, 668, 682, 686, 694, 696, 698, 724, 728, 736, 740, 754, 758, 772, 776, 802, 806, 874, 878, 934

Offset: 1

Author

Thomas Curtright, Jun 06 2016

Keywords

• nonn

Comments

The sequence is infinite only if the number of twin primes is infinite.

Note that not all even integers can be written as the sum of two twins (e.g. 94, 96, 98,...).

Examples

			6 = 3 + 3 is an element since (3,5) are twins, as is 8 = 5 + 3.
10 = 7 + 3 = 5 + 5 is not an element, since it is not uniquely resolved, even though the two resolutions both involve primes with twins.
		

Crossrefs

Cf. A129363, A007534.

Programs

Mathematica

ok[n_] := 1 == Length@ IntegerPartitions[n, {2}, Select[Prime@ Range@ PrimePi@ n, Or @@ PrimeQ[# + {-2, 2}] &]]; Select[2 Range[500], ok] (* Giovanni Resta, Jun 06 2016 *)

Extensions

a(7)-a(54) from Giovanni Resta, Jun 06 2016