

A023036


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


19



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
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OFFSET

0,1


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


LINKS

T. D. Noe and 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


EXAMPLE

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.
Triangle [Daniel Forgues, Jun 13 2014]:
4 = 2 + 2;
10 = 7 + 3 = 5 + 5;
22 = 19 + 3 = 17 + 5 = 11 + 11;
34 = 31 + 3 = 29 + 5 = 23 + 11 = 17 + 17;
48 = 43 + 5 = 41 + 7 = 37 + 11 = 31 + 17 = 29 + 19;
60 = 53 + 7 = 47 + 13 = 43 + 17 = 41 + 19 = 37 + 23 = 31 + 29.


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 *)


CROSSREFS

Cf. A045917, A000954.
Sequence in context: A179116 A036954 A109679 * A263661 A005306 A075898
Adjacent sequences: A023033 A023034 A023035 * A023037 A023038 A023039


KEYWORD

nonn,look


AUTHOR

David W. Wilson, Jun 14 1998


STATUS

approved



