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%I #15 Apr 23 2024 08:28:27
%S 0,0,1,2,1,2,4,3,2,3,3,6,4,2,7,5,3,6,5,7,7,7,7,7,5,3,10,10,6,8,9,9,9,
%T 7,4,13,9,6,15,7,7,14,11,10,11,9,12,16,9,7,12,13,11,15,14,13,17,12,7,
%U 16,11,8,23,12,9,17,14,16,18,15,15,21,12,10,17,19,16,20,16,11,22,15,14,27,14,11,29,20,12,18
%N a(n) = Sum_{primes p < n} r_2(n-p)/4, where r_2(n) = A004018(n).
%H Amiram Eldar, <a href="/A331136/b331136.txt">Table of n, a(n) for n = 1..10000</a>
%H Yoichi Motohashi, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa16/aa1633.pdf">On the distribution of prime numbers which are of the form x^2+y^2+1</a>, Acta Arith. 16 (1969/70), 351-363. MR0288086 (44 #5284).
%t a[n_] := Sum[SquaresR[2, n - p]/4, {p, Select[Range[n - 1], PrimeQ]}]; Array[a, 100] (* _Amiram Eldar_, Apr 23 2024 *)
%Y Cf. A004018, A331134.
%K nonn,changed
%O 1,4
%A _N. J. A. Sloane_, Jan 11 2020
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