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A130504 Number of k for which T(n) + T(k) is prime, with 0<=k<=n and triangular number T(n)=n(n+1)/2. 3

%I

%S 0,1,1,1,2,0,1,3,1,1,2,1,1,4,0,1,8,2,3,4,1,3,7,3,0,4,3,3,6,2,1,6,2,3,

%T 6,2,3,7,4,2,8,2,4,7,2,3,15,5,3,6,2,5,13,5,1,6,2,3,21,3,3,14,3,6,7,2,

%U 5,15,6,3,6,5,9,15,4,3,12,3,6,18,3,7,16,4,6,7,7,5,15,1,4,17,5,6,9,7,8,18,6,5

%N Number of k for which T(n) + T(k) is prime, with 0<=k<=n and triangular number T(n)=n(n+1)/2.

%C It appears that a(n)=0 for n=0,5,14,24 only. See A129634 for the least k.

%H T. D. Noe, <a href="/A130504/b130504.txt">Table of n, a(n) for n = 0..10000</a>

%e a(4)=2 because 10+1 and 10+3 are prime; a(7)=3 because 28+1, 28+3 and 28+15 are primes.

%t nn=100; tri=Range[0,nn]Range[nn+1]/2; Table[cnt=0; Do[If[PrimeQ[tri[[k]]+tri[[n]]], cnt++ ], {k,n}]; cnt, {n,Length[tri]}]

%Y Cf. A069004 (for square numbers).

%K nonn

%O 0,5

%A _T. D. Noe_, Jun 04 2007

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