

A231018


a(n) = d(n)/p(n1)# where d(n) > 0 is the common difference of the smallest pterm arithmetic progression of primes beginning with p = p(n) = nth prime.


2




OFFSET

1,4


COMMENTS

d(n) is the least d > 0 such that p, p+d, p+2d, ..., p+(p1)d are all prime with p = p(n), and p(n1)# = A002110(n1) is a primorial.
d(n) is always a multiple of p(n1)#.
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 5term AP beginning with 5, so a(3) = (115)/p(2)# = 6/2*3 = 1.


CROSSREFS

Cf. A002110, A088430, A231017.
Sequence in context: A269527 A111727 A277630 * A115738 A115763 A052000
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



