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

1,1

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A182315, A002144 (Pythagorean primes).

Sequence in context: A197912 A203114 A198027 * A009240 A180387 A324411

Adjacent sequences: A216921 A216922 A216923 * A216925 A216926 A216927

Keyword

nonn

Author

Thomas Ordowski, Sep 20 2012

Extensions

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

Status

approved