A080862 Numbers which can be expressed as the sum of two distinct primes in exactly six ways.

60, 66, 72, 100, 110, 116, 172, 178, 182, 194, 206, 212, 218, 226, 248, 278, 326, 332, 398

Offset

1,1

Comments

Apparently there are no further terms beyond 398. - R. J. Mathar, Oct 01 2021

Links

Table of n, a(n) for n=1..19.

Formula

{j: A117929(j) = 6}. - R. J. Mathar, Oct 01 2021

Example

66 is a term as 66 = 37 + 29 = 43 + 23 = 47 + 17 = 53 + 13 = 59 + 7 = 61 + 5 are only the six ways to express 66 as a sum of two distinct primes.

Mathematica

tdpQ[n_]:=Count[IntegerPartitions[n, {2}], _?(AllTrue[#, PrimeQ]&&Length[Union[#]]==2&)]==6; Select[Range[400], tdpQ] (* Harvey P. Dale, Aug 17 2025 *)

Crossrefs

Cf. A077914 (2 ways), A077969 (3 ways), A078299 (4 ways), A080854 (5 ways).

Sequence in context: A138690 A118155 A066722 * A239415 A106130 A216828

Adjacent sequences: A080859 A080860 A080861 * A080863 A080864 A080865

Keyword

nonn

Author

Shyam Sunder Gupta, Mar 29 2003

Status

approved