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A274001 Even numbers with a unique resolution as the sum of two primes, each of which has a twin. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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,...).

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A129363, A007534.

Sequence in context: A072057 A212351 A327240 * A324212 A160133 A057710

Adjacent sequences:  A273998 A273999 A274000 * A274002 A274003 A274004

KEYWORD

nonn

AUTHOR

Thomas Curtright, Jun 06 2016

EXTENSIONS

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

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)