A113044 Number of ways you can split the set of the first n primes into two proper subsets of which the sum of one is thrice the sum of the other.

0, 0, 0, 0, 2, 0, 0, 0, 5, 0, 11, 0, 0, 0, 75, 0, 203, 0, 558, 0, 1559, 0, 0, 0, 12786, 0, 37147, 0, 108491, 0, 321551, 0, 964713, 0, 2904950, 0, 8775407, 0, 0, 0, 0, 0, 0, 0, 760875083, 0, 0, 0, 7272292133, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2063638853745109

Offset

1,5

Links

Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 1..1000

Maple

A113044:=proc(n) local i, j, p, t; t:=0; for j from 2 to n do p:=1; for i to j do p:=p*(x^(-3*ithprime(i))+x^(ithprime(i))); od; t:=t, coeff(p, x, 0); od; t; end;
# second Maple program
sp:= proc(n) option remember; `if` (n=1, 2, sp(n-1) +ithprime(n)) end: b:= proc() option remember; local i, j, t; `if` (args[1]=0, `if` (nargs=2, 1, b(args[t] $t=2..nargs)), add (`if` (args[j] -ithprime (args[nargs]) <0, 0, b(sort ([seq (args[i] -`if` (i=j, ithprime (args[nargs]), 0), i=1..nargs-1)])[], args[nargs]-1)), j=1..nargs-1)) end: a:= proc(n) local m; m:= sp(n); `if` (irem(m, 4)=0, b(m/4, 3*m/4, n), 0) end: seq (a(n), n=1..70); # Alois P. Heinz, Nov 02 2011

Mathematica

d = {1}; nMax = 100; Lst = {};
Do[
  p = Prime[n];
  d = PadLeft[d, Length[d] + 4 p] + PadRight[d, Length[d] + 4 p];
  AppendTo[Lst, d[[-Ceiling[Length[d]/4]]]];
  , {n, 1, nMax}];
Lst(* Ray Chandler, Mar 09 2014 *)

Crossrefs

Cf. A022894.

Sequence in context: A153198 A182492 A222898 * A333792 A082399 A051883

Adjacent sequences: A113041 A113042 A113043 * A113045 A113046 A113047

Keyword

nonn

Author

Floor van Lamoen, Oct 12 2005

Extensions

More terms from Alois P. Heinz, Nov 02 2011

Status

approved