A216924 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.

5, 17, 113, 197, 461, 881, 1493, 1801, 39581, 50593, 78989, 180797, 183089, 241601, 250501, 268297, 339841, 485209, 492421, 618637, 919421, 1264337, 1561829, 1637813, 1994101, 2116129, 2191633, 2243909, 2314373, 3254929, 3422917, 3440621, 4468889, 4855297, 4874717, 5059321, 5526613, 6118769, 7856441, 9199153

Offset: 1

Author

Thomas Ordowski, Sep 20 2012

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A182315, A002144 (Pythagorean primes).

Programs

Mathematica

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 *)

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

Extensions

a(22)-a(40) from Charles R Greathouse IV, Sep 21 2012