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A023036 Smallest positive even integer that is an unordered sum of two primes in exactly n ways. 15

%I

%S 2,4,10,22,34,48,60,78,84,90,114,144,120,168,180,234,246,288,240,210,

%T 324,300,360,474,330,528,576,390,462,480,420,570,510,672,792,756,876,

%U 714,798,690,1038,630,1008,930,780,960,870,924,900,1134,1434,840,990,1302,1080

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

%C Except for first two terms, same as A001172.

%C The first occurrence of k in A045917.

%C The graph looks like a comet. - _Daniel Forgues_, Jun 12 2014

%H T. D. Noe and Robert G. Wilson v, <a href="/A023036/b023036.txt">Table of n, a(n) for n = 0..10000</a> (first 1001 terms from T. D. Noe)

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%e 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.

%e Triangle [_Daniel Forgues_, Jun 13 2014]:

%e 4 = 2 + 2;

%e 10 = 7 + 3 = 5 + 5;

%e 22 = 19 + 3 = 17 + 5 = 11 + 11;

%e 34 = 31 + 3 = 29 + 5 = 23 + 11 = 17 + 17;

%e 48 = 43 + 5 = 41 + 7 = 37 + 11 = 31 + 17 = 29 + 19;

%e 60 = 53 + 7 = 47 + 13 = 43 + 17 = 41 + 19 = 37 + 23 = 31 + 29.

%t 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_ *)

%Y Cf. A045917, A000954.

%K nonn,look

%O 0,1

%A _David W. Wilson_, Jun 14 1998

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Last modified October 18 23:05 EDT 2019. Contains 328211 sequences. (Running on oeis4.)