1,1

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.

Clark Kimberling, Table of n, a(n) for n = 1..500

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

3 ...... 5 ................ 3 + 2

4 ...... 7 ................ 5 + 2

6 ...... 13 ............... 11 + 2

8 ...... 19 ............... 17 + 2

35 ..... 149 .............. 139 + 7 + 3

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 *)

c = Table[Length[t[[n]][[2]]], {n, 2, z}] (* A242253 *)

f = 1 + Flatten[Position[tr, 0]] (* A242254 *)

Prime[f] (* A242255 *)

f1 = Prime[Complement[Range[Max[f]], f]] (* A242256 *)

(* Peter J. C. Moses, May 06 2014 *)

Cf. A242252, A242253, A242255, A242256, A241833, A000040.

Sequence in context: A325172 A365271 A390086 * A107770 A067054 A069357

Adjacent sequences: A242251 A242252 A242253 * A242255 A242256 A242257

nonn,easy

Clark Kimberling, May 09 2014

approved