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%I #18 Mar 13 2023 11:51:45
%S 0,1,1,2,3,2,2,3,3,5,6,5,6,2,7,5,6,8,7,7,7,12,10,10,11,11,12,10,10,12,
%T 11,13,10,10,10,10,9,8,7,9,3,4,4,4,11,13,15,17,19,19,22,19,16,13,17,
%U 16,15,16,14,17,16,21,24,19,19,13,17,17,19,19,16,11,13,13,22,19,19,17,22
%N (n-th 4k+1 prime minus n-th 4k+3 prime minus two)/4.
%C Zero occurs infinitely often as do the negative numbers.
%C First occurrence of a(n) beginning with 0: 1, 2, 4, 5, 42, 10, 11, 15, 18, 37, 23, 25, 22, 32, 59, 47, 53, 48, 83, 49, 110, 62, 51, 82, 63, 170, ...,
%C The first negative term is at n=1473. - _T. D. Noe_, Apr 09 2009
%H T. D. Noe, <a href="/A118480/b118480.txt">Table of n, a(n) for n=1..2000</a>
%F a(n) = (A002144(n) - A002145(n) - 2)/4.
%t (Select[1 + 4Range@245, PrimeQ@# &] - Select[ -1 + 4Range@225, PrimeQ@# &] - 2)/4
%Y Cf. A022757, A007350, A007351, A038691.
%K sign
%O 1,4
%A _Clark Kimberling_ and _Robert G. Wilson v_, May 04 2006