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%I #6 May 15 2014 10:14:18
%S 5,7,13,19,31,43,61,73,103,109,139,149,151,181,191,193,199,229,241,
%T 251,271,283,293,313,347,349,419,421,431,433,463,523,557,571,587,601,
%U 619,641,643,661,701,719,797,811,821,823,829,839,859,883,929,1021,1031
%N Primes-greedy summable primes, as defined at A242252.
%C See A242252 for the definitions of greedy sum and summability. A242255 and A242256 partition the primes.
%H Clark Kimberling, <a href="/A242255/b242255.txt">Table of n, a(n) for n = 1..500</a>
%e Four primes-greedy primes with matching prime-greedy sums are shown here:
%e a(1) = 5 = 3 + 2
%e a(2) = 7 = 5 + 2
%e a(3) = 13 = 11 + 2
%e a(12) = 149 = 139 + 7 + 3
%t z = 200; s = Table[Prime[n], {n, 1, z}]; t = Table[{s[[n]], #, Total[#] == s[[n]]} &[ DeleteCases[-Differences[FoldList[If[#1 - #2 >= 0, #1 - #2, #1] &, s[[n]], Reverse[Select[s, # < s[[n]] &]]]], 0]], {n, z}]; r[n_] := s[[n]] - Total[t[[n]][[2]]]; tr = Table[r[n], {n, 2, z}] (* A242252 *)
%t c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242253 *)
%t f = 1 + Flatten[Position[tr, 0]] (* A242254 *)
%t Prime[f] (* A242255 *)
%t f1 = Prime[Complement[Range[Max[f]], f]] (* A242256 *)
%t (* _Peter J. C. Moses_, May 06 2014 *)
%Y Cf. A242252, A242253, A242254, A242256, A241833, A000040.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, May 09 2014
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