A088683 a(n) = prime(3*n+2) - prime(3*n).

6, 6, 8, 6, 12, 10, 10, 12, 6, 18, 12, 12, 12, 12, 14, 6, 8, 12, 8, 12, 6, 20, 6, 14, 10, 12, 12, 10, 12, 16, 12, 18, 24, 12, 16, 8, 10, 22, 10, 14, 14, 18, 12, 14, 12, 22, 12, 12, 6, 18, 24, 18, 10, 18, 14, 16, 12, 16, 12, 22, 10, 14, 24, 18, 14, 10, 8, 28, 10, 10, 16, 40, 14, 24, 6

Offset: 1

Author

Zak Seidov, Oct 05 2003

Keywords

• easy
• nonn

Comments

Previous name was: Differences in triples of primes.

Minimal difference is 6 (for 3-tuplet) except first triple. Repeating 6 means successive 3-tuplets, see A088683, A088684..

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088680, A078584, A088682, A088684.

Programs

Magma

[NthPrime(3*n+2) - NthPrime(3*n): n in [1..80]]; // G. C. Greubel, May 19 2019

Mathematica

#[[3]]-#[[1]]&/@Partition[Prime[Range[3,300]],3]  (* Harvey P. Dale, Jan 12 2011 *)

PARI

a(n) = prime(3*n+2) - prime(3*n); \\ Michel Marcus, Oct 05 2013

Sage

[nth_prime(3*n+2) - nth_prime(3*n) for n in (1..80)] # G. C. Greubel, May 19 2019

Formula

Partition primes in triples starting with 5: {5, 7, 11}, {13, 17, 19}, {23, 29, 31}, {37, 41, 43}, {47, 53, 59}, {61, 67, 71}, {73, 79, 83}, {89, 97, 101}, {103, 107, 109}. Sequence gives differences between lesser and larger primes in triples.

Extensions

New name from Michel Marcus, Oct 05 2013