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A113043 Number of ways you can split the set of the first n primes into two proper subsets of which the sum of one is twice the sum of the other. 1

%I

%S 0,0,0,0,0,0,0,0,0,11,0,0,0,0,0,255,0,766,0,2342,0,0,0,23373,0,75005,

%T 0,243824,0,800249,0,2643880,0,8789565,0,29396169,0,0,0,333867426,0,

%U 1132658742,0,3858864902,0,13182921033,0,0,0,0,0,537690715092,0

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

%H Alois P. Heinz and Ray Chandler, <a href="/A113043/b113043.txt">Table of n, a(n) for n = 1..1000</a>

%p A113043:=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^(-2*ithprime(i))+x^(ithprime(i))); od; t:=t,coeff(p,x,0); od; t; end;

%p # second Maple program:

%p 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,3)=0, b(m/3, 2*m/3, n),0) end: seq(a(n), n=1..70); # _Alois P. Heinz_, Sep 06 2009

%t d = {1}; nMax = 100; Lst = {};

%t Do[

%t p = Prime[n];

%t d = PadLeft[d, Length[d] + 3 p] + PadRight[d, Length[d] + 3 p];

%t AppendTo[Lst, d[[-Ceiling[Length[d]/3]]]];

%t , {n, 1, nMax}];

%t Lst (* _Ray Chandler_, Mar 09 2014 *)

%Y Cf. A022894.

%K nonn

%O 1,10

%A _Floor van Lamoen_, Oct 12 2005

%E Extended beyond a(40) by _Alois P. Heinz_, Sep 06 2009

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Last modified August 24 22:38 EDT 2019. Contains 326314 sequences. (Running on oeis4.)