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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
 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, 0, 243824, 0, 800249, 0, 2643880, 0, 8789565, 0, 29396169, 0, 0, 0, 333867426, 0, 1132658742, 0, 3858864902, 0, 13182921033, 0, 0, 0, 0, 0, 537690715092, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,10 LINKS Alois P. Heinz and Ray Chandler, Table of n, a(n) for n = 1..1000 MAPLE 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; # 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, 3)=0, b(m/3, 2*m/3, n), 0) end: seq(a(n), n=1..70); # Alois P. Heinz, Sep 06 2009 MATHEMATICA d = {1}; nMax = 100; Lst = {}; Do[   p = Prime[n];   d = PadLeft[d, Length[d] + 3 p] + PadRight[d, Length[d] + 3 p];   AppendTo[Lst, d[[-Ceiling[Length[d]/3]]]];   , {n, 1, nMax}]; Lst (* Ray Chandler, Mar 09 2014 *) CROSSREFS Cf. A022894. Sequence in context: A321538 A321803 A321797 * A110408 A179920 A216726 Adjacent sequences:  A113040 A113041 A113042 * A113044 A113045 A113046 KEYWORD nonn AUTHOR Floor van Lamoen, Oct 12 2005 EXTENSIONS Extended beyond a(40) by Alois P. Heinz, Sep 06 2009 STATUS approved

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Last modified July 20 23:29 EDT 2019. Contains 325189 sequences. (Running on oeis4.)