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

1,1

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A000040, A072473.

Sequence in context: A089174 A321700 A020636 * A265760 A071200 A038921

Adjacent sequences: A141654 A141655 A141656 * A141658 A141659 A141660

Keyword

nonn

Author

Juri-Stepan Gerasimov, Sep 18 2008

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

Status

approved