A071695 Lesser members of twin prime pairs of form (4*k+1, 4*k+3), k > 0.

5, 17, 29, 41, 101, 137, 149, 197, 269, 281, 461, 521, 569, 617, 641, 809, 821, 857, 881, 1049, 1061, 1229, 1277, 1289, 1301, 1481, 1697, 1721, 1877, 1949, 1997, 2081, 2129, 2141, 2237, 2309, 2381, 2549, 2657, 2729, 2789, 2801, 2969

Offset: 1

Author

Reinhard Zumkeller, Jun 04 2002

Keywords

• nonn

Comments

Corresponding greater members: A071696(n).

Or, lesser members of twin prime pairs (A001359) which are also Pythagorean primes (A002144). Intersection of A001359 and A002144. - Zak Seidov, Apr 25 2008

A010051(a(n)) * A010051(a(n)+2) = 1. - Reinhard Zumkeller, Nov 10 2013

Links

• Zak Seidov, Table of n, a(n) for n = 1..1000.
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Crossrefs

Cf. A001359, A002144, A071698, A071697.

Programs

Haskell

a071695 n = a071695_list !! (n-1)
a071695_list = [p | p <- a002144_list, a010051' (p + 2) == 1]
-- Reinhard Zumkeller, Nov 10 2013

Mathematica

Select[ Prime@ Range@ 1000, Mod[#, 4] == 1 && PrimeQ[# + 2] &] (* Robert G. Wilson v, Jan 22 2012 *)

PARI

p=2;forprime(q=3,1e4,if(q-p==2 && p%4==1, print1(p", "));p=q) \\ Charles R Greathouse IV, Mar 20 2013