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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A082399 A051883 A132792 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

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Last modified July 19 09:33 EDT 2019. Contains 325155 sequences. (Running on oeis4.)