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%I #7 Dec 25 2016 00:37:23
%S 1,6,9,15,17,21,31,27,35,33,39,41,45,47,55,51,53,57,242,63,67,65,71,
%T 476,79,81,578,85,77,83,99,572,512,89,97,95,103,111,101,692,1040,632,
%U 115,107,782,129,121,113,902,141,119,842,992,125,133,147,1520,131,159,145
%N First occurrence of n in A068307: least number k such that the number of decomposition of k into the sum of three primes is n.
%C Records (differs from A139322): 1, 6, 9, 15, 17, 21, 31, 35, 39, 41, 45, 47, 55, 57, 242, 476, 578, 692, 1040, 1520, 1898, 2162, 2480, 3536, 4004, 4034, 4526, 5456, 5918, 7010, 8804, 9740, 10106, 10262, 10412, 10622, 10772, 10952, 11462, 12362, 12452, 12512, 12560, 12662, 12902, ... .
%H Robert G. Wilson v and T. D. Noe, <a href="/A139321/b139321.txt">Table of n, a(n) for n = 0..2500</a>
%t f[n_] := Block[{c = 0, lmt = PrimePi@ Floor[n/2], p, q}, Do[p = Prime@ i; q = Prime@ j; r = n - p - q; If[ PrimeQ@ r && r >= p, c++ ], {i, lmt}, {j, i}]; c]; t = Table[0, {1000}]; Do[a = f@n; If[t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 10^6}]
%Y Cf. A000040, A068307. Records: A139322.
%K nonn
%O 0,2
%A _Robert G. Wilson v_, Apr 13 2008
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