login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 A265811

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 6 03:02 EST 2016. Contains 278771 sequences.