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

Author

Floor van Lamoen, Oct 12 2005

Keywords

• nonn

Links

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

Crossrefs

Cf. A022894.

Programs

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 *)

Extensions

More terms from Alois P. Heinz, Nov 02 2011