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A053647 First term of first sequence of n primes in arithmetic progression with a common difference equal to the product of first n primes. 0
2, 5, 7, 13, 37, 73, 7937, 7703, 272809, 640943, 5378959, 116137159, 3708797237, 114649314209, 158317270283 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..15.

R. Chapman, Dirichlet's theorem:a real variable approach

B. Green & T. Tao, The primes contain arbitrarily long arithmetic progressions

Index entries for sequences related to primes in arithmetic progressions

EXAMPLE

For n=3, product of first 3 primes is 30. The first arithmetic progression of 3 primes with difference 30 starts at 7 (7, 37, 67), so a(3)=7.

MATHEMATICA

(* This program is not convenient beyond 10 terms *) r[p1_, n_] := Reduce[p[1] = p1; Equal @@ Append[Table[p[k + 1] - p[k], {k, 1, n - 1}], Product[Prime[k], {k, 1, n}]], p[2], Primes]; a[n_] := a[n] = Catch[For[k = 1, k <= 10^5, k++, If[r[p1 = Prime[k], n] =!= False, Throw[p1]]]]; Table[Print[a[n]]; a[n], {n, 1, 10}] (* Jean-Fran├žois Alcover, Dec 27 2012 *)

CROSSREFS

Sequence in context: A177997 A238776 A141112 * A023242 A164570 A126338

Adjacent sequences:  A053644 A053645 A053646 * A053648 A053649 A053650

KEYWORD

hard,nonn,nice

AUTHOR

G. L. Honaker, Jr., Feb 18 2000

EXTENSIONS

Last 3 terms from Jud McCranie, Feb 28 2000

a(14)>2^32 and a(15)>2^32 - Jud McCranie.

a(14)-a(15) from Donovan Johnson, Oct 20 2009

STATUS

approved

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Last modified November 21 11:17 EST 2014. Contains 249777 sequences.