A023036 Smallest positive even integer that is an unordered sum of two primes in exactly n ways.

2, 4, 10, 22, 34, 48, 60, 78, 84, 90, 114, 144, 120, 168, 180, 234, 246, 288, 240, 210, 324, 300, 360, 474, 330, 528, 576, 390, 462, 480, 420, 570, 510, 672, 792, 756, 876, 714, 798, 690, 1038, 630, 1008, 930, 780, 960, 870, 924, 900, 1134, 1434, 840, 990, 1302, 1080

Offset: 0

Author

David W. Wilson, Jun 14 1998

Keywords

• nonn
• look

Comments

Except for first two terms, same as A001172.

The first occurrence of k in A045917.

The graph looks like a comet. - Daniel Forgues, Jun 12 2014

Examples

			a(3) = 22 as 22 = (19+3) = (17+5) = (11+11). There are exactly 3 ways 22 can be expressed as the sum of two primes and no even number less than 22 can be so expressed.
From _Daniel Forgues_, Jun 13 2014: (Start)
Terms for n = 1..6 and corresponding sums:
  a(1) =  4 =  2 + 2;
  a(2) = 10 =  7 + 3 =  5 +  5;
  a(3) = 22 = 19 + 3 = 17 +  5 = 11 + 11;
  a(4) = 34 = 31 + 3 = 29 +  5 = 23 + 11 = 17 + 17;
  a(5) = 48 = 43 + 5 = 41 +  7 = 37 + 11 = 31 + 17 = 29 + 19;
  a(6) = 60 = 53 + 7 = 47 + 13 = 43 + 17 = 41 + 19 = 37 + 23 = 31 + 29.
(End)
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..10000 (first 1001 terms from T. D. Noe)
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A045917, A000954, A136244, A258713.

Programs

Mathematica

f[n_] := Length@ Select[2n - Prime@ Range@ PrimePi@ n, PrimeQ]; nn = 100; t = Table[0, {nn}]; k = 1; cnt = 0; While[cnt < nn, a = f@k; If[a <= nn && t[[a]] == 0, t[[a]] = 2 k; cnt++]; k++]; t (* Robert G. Wilson v, Mar 15 2011 *)