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%I #7 Aug 28 2016 18:18:35
%S 2,1,0,1,1,7,4,1,1,7,3,1,1,3,16,13,1,4,4,1,1,4,4,1,46,3,7,1,2,7,16,2,
%T 13,4,3,1,13,3,4,22,1,16,16,1,1,7,3,1,10,3,7,1,2,7,16,2,1,4,4,13,1,4,
%U 16,1,1,16,4,2,1,16,8,1,10,3,7,1,1,31,7,2,13,4,4,10,1,8,7,13,1,43,16,5,25,16
%N Least nonnegative m such that T(n) + T(m) is prime, where T(n) = n(n+1)/2.
%C What is the simplest proof that this is defined for all nonzero n?
%C It appears that a(n)<n except for n=0,5,14,24. The graph of A130504 provides evidence that a(n) exists for all n. - _T. D. Noe_, Jun 04 2007
%H T. D. Noe, <a href="/A129634/b129634.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = Min{m: m*(m+1)/2 + n*(n+1)/2 is prime}. a(n) = Min{m: A000217(m) + A000217(n) is an element of A000040}.
%e a(6) = 4 because T(4) = 10 is the least triangular number whose sum with T(6) = 21 is prime, since {21+0 = 3*7, 21+3 = 2^3*3, 21+6 = 3^3} are all composite, but 21+10 = 31 is prime.
%t nn=100; tri=Range[0,nn]Range[nn+1]/2; Table[k=1; While[k<=Length[tri] && !PrimeQ[tri[[k]]+tri[[n]]], k++ ]; If[k<=Length[tri], k-1,0], {n,Length[tri]}] - _T. D. Noe_, Jun 04 2007
%Y Cf. A000040, A000217, A129755, A130334.
%Y Cf. A069003 (for square numbers).
%K easy,nonn
%O 0,1
%A _Jonathan Vos Post_, May 31 2007
%E Corrected and extended by _T. D. Noe_, Jun 04 2007
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