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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

%I #11 Mar 02 2015 16:08:50

%S 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,

%T 37147,0,108491,0,321551,0,964713,0,2904950,0,8775407,0,0,0,0,0,0,0,

%U 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

%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 thrice the sum of the other.

%H Alois P. Heinz and Ray Chandler, <a href="/A113044/b113044.txt">Table of n, a(n) for n = 1..1000</a>

%p 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;

%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, 4)=0, b(m/4, 3*m/4, n), 0) end: seq (a(n), n=1..70); # _Alois P. Heinz_, Nov 02 2011

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

%t Do[

%t p = Prime[n];

%t d = PadLeft[d, Length[d] + 4 p] + PadRight[d, Length[d] + 4 p];

%t AppendTo[Lst, d[[-Ceiling[Length[d]/4]]]];

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

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

%Y Cf. A022894.

%K nonn

%O 1,5

%A _Floor van Lamoen_, Oct 12 2005

%E More terms from _Alois P. Heinz_, Nov 02 2011

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)