A141657 a(n) = (prime(2*m)-prime(m))/6 where m is the n-th positive integer such that (prime(2*m)-prime(m))/6 is prime.

2, 3, 7, 11, 13, 17, 19, 23, 71, 71, 83, 83, 89, 101, 103, 127, 163, 167, 191, 193, 199, 239, 239, 251, 263, 277, 307, 307, 307, 317, 331, 337, 389, 443, 463, 487, 509, 509, 557, 659, 691, 787, 797, 863, 881, 883, 887, 887, 953, 971, 977, 991, 1019, 1063, 1069

Offset: 1

Author

Juri-Stepan Gerasimov, Sep 18 2008

Keywords

• nonn

Examples

			For m=4,  (p(2*4)  - p(4))/6  =  (19 -  7)/6 =  2 = a(1).
For m=5,  (p(2*5)  - p(5))/6  =  (29 - 11)/6 =  3 = a(2).
For m=10, (p(2*10) - p(10))/6 =  (71 - 29)/6 =  7 = a(3).
For m=15, (p(2*15) - p(15))/6 = (113 - 47)/6 = 11 = a(4).
For m=16, (p(2*16) - p(16))/6 = (131 - 53)/6 = 13 = a(5), etc.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A072473.

Programs

Mathematica

Select[Table[(Prime[2n]-Prime[n])/6,{n,1000}],PrimeQ[#]&] (* Harvey P. Dale, Jun 18 2023 *)

Extensions

19, 23 inserted, one instance of 331 removed, 577 removed and extended by R. J. Mathar, Oct 04 2008

Definition clarified by Harvey P. Dale, Jun 18 2023

Definition clarified by David A. Corneth, Jun 18 2023