|
%I #49 Nov 03 2023 06:37:57
%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 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 From _Daniel Forgues_, Jun 13 2014: (Start)
%e Terms for n = 1..6 and corresponding sums:
%e a(1) = 4 = 2 + 2;
%e a(2) = 10 = 7 + 3 = 5 + 5;
%e a(3) = 22 = 19 + 3 = 17 + 5 = 11 + 11;
%e a(4) = 34 = 31 + 3 = 29 + 5 = 23 + 11 = 17 + 17;
%e a(5) = 48 = 43 + 5 = 41 + 7 = 37 + 11 = 31 + 17 = 29 + 19;
%e a(6) = 60 = 53 + 7 = 47 + 13 = 43 + 17 = 41 + 19 = 37 + 23 = 31 + 29.
%e (End)
%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_, Mar 15 2011 *)
%Y Cf. A045917, A000954, A136244, A258713.
%K nonn,look
%O 0,1
%A _David W. Wilson_, Jun 14 1998
|
