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Numbers k such that the k-th prime is primes-greedy summable, as defined at A242252.
5

%I #6 May 15 2014 10:14:10

%S 3,4,6,8,11,14,18,21,27,29,34,35,36,42,43,44,46,50,53,54,58,61,62,65,

%T 69,70,81,82,83,84,90,99,102,105,107,110,114,116,117,121,126,128,139,

%U 141,142,143,145,146,149,153,158,172,173,174,176,177,178,179,183

%N Numbers k such that the k-th prime is primes-greedy summable, as defined at A242252.

%C See A242252 for the definitions of greedy sum and summability. a(n) is the index for the n-th primes-greedy summable prime; those primes are given at A242255.

%H Clark Kimberling, <a href="/A242254/b242254.txt">Table of n, a(n) for n = 1..500</a>

%e a(n) ... a(n)-th prime .... primes-greedy sum

%e 3 ...... 5 ................ 3 + 2

%e 4 ...... 7 ................ 5 + 2

%e 6 ...... 13 ............... 11 + 2

%e 8 ...... 19 ............... 17 + 2

%e 35 ..... 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, A242255, A242256, A241833, A000040.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, May 09 2014