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%I #14 Apr 24 2021 04:14:50
%S 2,1,3,2,1,3,2,3,4,2,1,2,1,6,3,2,4,2,3,1,8,1,2,4,3,2,1,3,5,1,5,3,1,5,
%T 4,2,1,2,3,3,4,2,1,12,3,5,4,3,2,4,2,3,1,6,3,2,3,1,6,2,6,6,1,2,1,6,3,3,
%U 2,6,1,5,1,12,2,1,3,6,5,3,1,2,3,4,3,2,6,1,3,2,3,6,7,3,2,3,1,3,2,3,7,3,2,1,5
%N One quarter of first differences of primes of the form 4*k+1 (A002144).
%H Amiram Eldar, <a href="/A082074/b082074.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A002144(n+1) - A002144(n))/4.
%e The first and second primes of the form 4*k+1 are 5 and 13, so a(1) = (13-5)/4 = 2.
%t k=0; m=4; r=1; 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[4*Range[1000]+1,PrimeQ]]/4 (* _Harvey P. Dale_, Dec 04 2011 *)
%Y Cf. A002144, A002145, A082073, A082075, A082076.
%K nonn
%O 1,1
%A _Labos Elemer_, Apr 07 2003
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