A231018 a(n) = d(n)/p(n-1)# where d(n) > 0 is the common difference of the smallest p-term arithmetic progression of primes beginning with p = p(n) = n-th prime.

1, 1, 1, 5, 7315048, 4293861989, 11387819007325752, 4244193265542951705

Offset

1,4

Comments

d(n) is the least d > 0 such that p, p+d, p+2d, ..., p+(p-1)d are all prime with p = p(n), and p(n-1)# = A002110(n-1) is a primorial.

d(n) is always a multiple of p(n-1)#.

a(5) and a(6) are due to G. Loh in 1986, and a(7) to Phil Carmody in 2001.

See A088430 and A231017 for more comments, references, links, and examples.

Links

Table of n, a(n) for n=1..8.

Index entries for sequences related to primes in arithmetic progressions

Formula

a(n) = A088430(n) / A002110(n) = (A231017(n) - prime(n)) / A002110(n).

Example

Prime(3) = 5 and 5, 11, 17, 23, 29 is the smallest 5-term AP beginning with 5, so a(3) = (11-5)/p(2)# = 6/2*3 = 1.

Crossrefs

Cf. A002110, A088430, A231017.

Sequence in context: A269527 A111727 A277630 * A115738 A115763 A383321

Adjacent sequences: A231015 A231016 A231017 * A231019 A231020 A231021

Keyword

nonn,hard,more

Author

Jonathan Sondow, Nov 08 2013

Extensions

a(8) due to Wojciech Izykowski in 2014 added by Jonathan Sondow, Aug 08 2019

Status

approved