A242254 Numbers k such that the k-th prime is primes-greedy summable, as defined at A242252.

3, 4, 6, 8, 11, 14, 18, 21, 27, 29, 34, 35, 36, 42, 43, 44, 46, 50, 53, 54, 58, 61, 62, 65, 69, 70, 81, 82, 83, 84, 90, 99, 102, 105, 107, 110, 114, 116, 117, 121, 126, 128, 139, 141, 142, 143, 145, 146, 149, 153, 158, 172, 173, 174, 176, 177, 178, 179, 183

Offset

1,1

Comments

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.

Links

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

Example

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

Mathematica

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 *)

Crossrefs

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

Sequence in context: A156040 A325172 A365271 * A107770 A067054 A039893

Adjacent sequences: A242251 A242252 A242253 * A242255 A242256 A242257

Keyword

nonn,easy

Author

Clark Kimberling, May 09 2014

Status

approved