A089450 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3 are consecutive primes, where p(i) denotes the i-th prime. Sequence terms are 2*p(k) + 3.

389, 449, 3217, 31469, 79757, 127297, 130817, 136417, 145349, 168601, 179957, 193577, 198277, 205069, 207377, 231677, 255617, 287137, 300749, 384001, 409589, 515737, 648437, 689917, 750509, 824069, 854869, 982301, 1103437, 1190237

Offset: 1

Author

Ray Chandler, Nov 03 2003

Keywords

• nonn

Examples

			p(44)=193, 2*193 + 3 = 389 = p(77);
p(45)=197, 2*197 + 3 = 397 = p(78);
p(46)=199, 2*199 + 3 = 401 = p(79).
		

Crossrefs

Subsequence of A089528.

Cf. A088066, A088119, A089525.

Programs

Mathematica

cpQ[n_]:=Module[{p1=2n+3,p2=2NextPrime[n]+3,p3=2NextPrime[n,2]+3,pr = PrimePi[ 2n+3]},{p1,p2,p3}==Prime[Range[pr,pr+2]]]; 2#+3&/@ Select[ Prime[ Range[50000]],cpQ] (* Harvey P. Dale, Sep 24 2019 *)

Formula

a(n) = 2*A088119(n) + 3 = 2*A000040(A088066(n)) + 3 = A000040(A089525(n)).

Extensions

Definition clarified by Harvey P. Dale, Sep 24 2019

Offset changed to 1 by Jinyuan Wang, Aug 04 2021