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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

%I

%S 1,1,1,5,7315048,4293861989,11387819007325752

%N 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.

%C 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.

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

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

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

%H <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>

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

%e 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.

%Y Cf. A002110, A088430, A231017.

%K hard,more,nonn

%O 1,4

%A _Jonathan Sondow_, Nov 08 2013

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Last modified May 24 04:25 EDT 2019. Contains 323528 sequences. (Running on oeis4.)