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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, 4244193265542951705 (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 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 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

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Last modified September 18 10:31 EDT 2020. Contains 337166 sequences. (Running on oeis4.)