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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. 2
1, 1, 1, 5, 7315048, 4293861989, 11387819007325752 (list; graph; refs; listen; history; text; internal format)
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..7.

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 A052000

Adjacent sequences:  A231015 A231016 A231017 * A231019 A231020 A231021

KEYWORD

hard,more,nonn

AUTHOR

Jonathan Sondow, Nov 08 2013

STATUS

approved

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Last modified April 18 06:48 EDT 2019. Contains 322209 sequences. (Running on oeis4.)