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%I #19 May 13 2013 01:54:22
%S 5,17,113,197,461,881,1493,1801,39581,50593,78989,180797,183089,
%T 241601,250501,268297,339841,485209,492421,618637,919421,1264337,
%U 1561829,1637813,1994101,2116129,2191633,2243909,2314373,3254929,3422917,3440621,4468889,4855297,4874717,5059321,5526613,6118769,7856441,9199153
%N Consecutive Pythagorean primes p = A002144(r) and q = A002144(r+1) such that q - p > log(p)^2. The number a(n) is the n-th value of p.
%H Charles R Greathouse IV, <a href="/A216924/b216924.txt">Table of n, a(n) for n = 1..10000</a>
%t t = {}; p = 5; Do[While[q = p; While[p = NextPrime[p]; Mod[p, 4] == 3]; p - q < Log[q]^2]; AppendTo[t, q], {25}]; t (* _T. D. Noe_, Sep 21 2012 *)
%o (PARI) r=1;v=List();p=5;forprime(q=11,1e7,if(q%4>1,next);if(q-p>r, r=log(p)^2\1; if(q-p>r,print1(p", ");listput(v,p)));p=q); Vec(v) \\ _Charles R Greathouse IV_, Sep 21 2012
%Y Cf. A182315, A002144 (Pythagorean primes).
%K nonn
%O 1,1
%A _Thomas Ordowski_, Sep 20 2012
%E a(22)-a(40) from _Charles R Greathouse IV_, Sep 21 2012