A242253 Number of primes in the primes-greedy sum (defined at A242252) for the n-th odd prime.

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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2

Offset

1,2

Comments

See A242252 for the definition of primes-greedy sum.

Links

Clark Kimberling, Table of n, a(n) for n = 1..2000

Example

n ... n-th odd prime .. primes-greedy sum... a(n)
2 ... 5 ............... 3 + 2 .............. 2
3 ... 7 ............... 5 + 2 .............. 2
4 ... 11 .............. 7 + 3 .............. 2
5 ... 13 .............. 11 + 2 ............. 2
34 .. 149 ............. 139 + 7 + 3 ........ 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, A242254, A242255, A242256, A241833, A000040.

Sequence in context: A076303 A339276 A343356 * A071839 A235044 A163857

Adjacent sequences: A242250 A242251 A242252 * A242254 A242255 A242256

Keyword

nonn,easy

Author

Clark Kimberling, May 09 2014

Status

approved