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A071695 Lesser members of twin prime pairs of form (4*k+1, 4*k+3), k > 0. 13
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

MATHEMATICA

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

PROG

(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

(Haskell)

a071695 n = a071695_list !! (n-1)

a071695_list = [p | p <- a002144_list, a010051' (p + 2) == 1]

-- Reinhard Zumkeller, Nov 10 2013

CROSSREFS

Cf. A001359, A002144, A071698, A071697.

Sequence in context: A126193 A074965 A145475 * A242025 A027703 A075695

Adjacent sequences:  A071692 A071693 A071694 * A071696 A071697 A071698

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jun 04 2002

STATUS

approved

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Last modified January 20 05:32 EST 2020. Contains 331067 sequences. (Running on oeis4.)