cp's OEIS Frontend

A235614 Number of ordered ways to write n = k + m with k a term of A235592 and m a positive triangular number.

%I A235614 #11 Jan 13 2014 01:23:24
%S A235614 0,0,1,1,2,2,2,2,3,2,2,4,1,3,3,2,3,3,3,3,5,2,3,5,3,3,3,2,4,6,2,4,3,2,
%T A235614 4,4,4,2,6,4,4,6,2,5,2,3,7,5,4,4,6,1,2,6,5,4,5,4,5,5,1,4,7,5,5,4,2,3,
%U A235614 5,4,4,8,4,6,4,4,4,1,2,4,7,5,3,5,3,5,3,2,6,6,4,6,8,1,4,5,5,4,7,6
%N A235614 Number of ordered ways to write n = k + m with k a term of A235592 and m a positive triangular number.
%C A235614 Conjecture: a(n) > 0 for all n > 2.
%H A235614 Zhi-Wei Sun, <a href="/A235614/b235614.txt">Table of n, a(n) for n = 1..10000</a>
%e A235614 a(13) = 1 since 13 = 3 + 10 with 3*4 - prime(3) = 7 prime and 10 = 4*5/2 a positive triangular number.
%e A235614 a(52) = 1 since 52 = 37 + 15 with 37*38 - prime(37) = 1249 prime and 15 = 5*6/2 a positive triangular number.
%e A235614 a(61) = 1 since 61 = 6 + 55 with 6*7 - prime(6) = 29 prime and 55 = 10*11/2 a positive triangular number.
%e A235614 a(313) = 1 since 313 = 37 + 276 with 37*38 - prime(37) = 1249 prime and 276 = 23*24/2 a positive triangular number.
%t A235614 PQ[n_]:=PrimeQ[n(n+1)-Prime[n]]
%t A235614 TQ[n_]:=IntegerQ[Sqrt[8n+1]]
%t A235614 a[n_]:=Sum[If[PQ[k]&&TQ[n-k],1,0],{k,1,n-1}]
%t A235614 Table[a[n],{n,1,100}]
%Y A235614 Cf. A000040, A000217, A235592, A235613.
%K A235614 nonn
%O A235614 1,5
%A A235614 _Zhi-Wei Sun_, Jan 13 2014