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%I #5 Mar 30 2012 18:49:34
%S 0,1,0,2,0,2,3,2,1,2,4,0,1,3,5,3,5,6,4,3,0,7,6,7,0,6,4,2,8,6,5,4,2,8,
%T 3,8,9,0,1,7,8,3,10,9,2,5,10,9,6,0,11,2,8,9,12,6,12,11,0,2,7,13,4,9,12
%N a(n)*(a(n)+1) + A002973(n)^2 = A005098(n), n>=1.
%C See the Jon Perry comment on A005098. The (even) promic number a(n)*(a(n)+1) (see A002378) when subtracted from A005098(n) (the n-th value k such that 4*k+1 is prime) leaves a square, namely A002973(n)^2. E.g., n=4: 7 - 2*3 = 1^1. n=5: 9 - 0 = 3^2.
%C 2*a(n)+1 = A002972(n), n>=1. E.g., n=4: 2*2+1=5.
%F a(n) = (sqrt(4*(k(n) - m(n)^2)+1)-1)/2, n>=1, with k(n) := A005098(n) (4*k(n)+1 is the prime A002144(n)) and m(n):= A002973(n).
%F a(n) = (A002972(n)-1)/2, n>=1.
%Y Cf. A005098, A002144, A002972, A002973, A002378.
%K nonn
%O 1,4
%A _Wolfdieter Lang_, Mar 01 2012
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