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%I #7 May 15 2014 10:13:43
%S 1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,
%T 2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,2,2,2,3,2,2,2,2,2,2,2,3,2,2,2,2,2,2,3,
%U 2,2,2,2,2,2,2,2,2,2,2,3,2,3,2,2,2,2
%N Number of primes in the primes-greedy sum (defined at A242252) for the n-th odd prime.
%C See A242252 for the definition of primes-greedy sum.
%H Clark Kimberling, <a href="/A242253/b242253.txt">Table of n, a(n) for n = 1..2000</a>
%e n ... n-th odd prime .. primes-greedy sum... a(n)
%e 2 ... 5 ............... 3 + 2 .............. 2
%e 3 ... 7 ............... 5 + 2 .............. 2
%e 4 ... 11 .............. 7 + 3 .............. 2
%e 5 ... 13 .............. 11 + 2 ............. 2
%e 34 .. 149 ............. 139 + 7 + 3 ........ 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, A242254, A242255, A242256, A241833, A000040.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, May 09 2014
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