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%I #14 Mar 26 2020 18:01:05
%S 8,4,12,8,4,12,8,12,16,8,4,8,4,24,12,8,16,8,12,4,32,4,8,16,12,8,4,12,
%T 20,4,20,12,4,20,16,8,4,8,12,12,16,8,4,48,12,20,16,12,8,16,8,12,4,24,
%U 12,8,12,4,24,8,24,24,4,8,4,24,12,12,8,24,4,20,4,48,8,4,12,24,20,12,4,8,12
%N First difference set of primes with 4k+1 form: A002144.
%C a(n) is divisible by 4, for all n.
%H Charles R Greathouse IV, <a href="/A082073/b082073.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A002144(n+1) - A002144(n).
%e first and second 4k+1 primes are 5 and 13, so a(1)=13-5=8;
%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)]; ], {n, 1, 1000}]
%t Differences[Select[Prime[Range[200]],Mod[#,4]==1&]] (* _Harvey P. Dale_, Feb 05 2020 *)
%o (PARI) p=5;forprime(q=7,1e3,if(q%4==1,print1(q-p", ");p=q)) \\ _Charles R Greathouse IV_, May 13 2012
%Y Cf. A002144, A002145, A082074, A082075, A082076.
%K nonn,easy
%O 1,1
%A _Labos Elemer_, Apr 07 2003
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