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%I #15 Apr 29 2022 18:09:25
%S 1,1,2,1,2,3,1,3,2,1,2,1,5,1,5,1,2,3,3,1,3,3,2,3,3,1,3,3,3,2,3,6,1,5,
%T 4,3,2,3,1,9,3,2,1,5,1,3,2,1,2,1,5,6,4,2,4,3,2,3,3,3,1,3,6,2,7,2,3,1,
%U 2,9,6,3,1,3,5,1,5,1,5,1,2,7,5,1,3,2,7,3,2,3,3,6,1,3,5,7,3,2,4,9,2,7,5,1,2
%N First differences of primes of the form 4*k+3 (A002145), divided by 4.
%H Amiram Eldar, <a href="/A082076/b082076.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A002145(n+1) - A002145(n))/4.
%e The first and second primes of the form 4*k+3 are 3 and 7, so a(1) = (7-3)/4 = 1.
%t k=0; m=4; r=3; Do[s=Mod[Prime[n], m]; If[Equal[s, r], rp=ep; k=k+1; ep=Prime[n]; Print[(ep-rp)/4]; ], {n, 1, 1000}]
%t Differences[Select[Prime[Range[400]],IntegerQ[(#-3)/4]&]]/4 (* _Harvey P. Dale_, Apr 29 2022 *)
%Y Cf. A002144, A002145, A082073, A082074, A082075.
%K nonn
%O 1,3
%A _Labos Elemer_, Apr 07 2003