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A121940 Product of the first n primes of the form 6n+1. 8
7, 91, 1729, 53599, 1983163, 85276009, 5201836549, 348523048783, 25442182561159, 2009932422331561, 194963444966161417, 20081234831514625951, 2188854596635094228659, 277984533772656967039693 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) + 2 is always divisible by 3. a(n) - 2 is prime for n = 1, 2, 4, 6, 40, 61.

See A002476 = Primes of form 6n + 1 for comments on equivalent definitions. Note that A006512 (Greater of twin primes) is a subset of A002476.

For n>1, a(n) is the least positive integer that can be primitively represented as m^2+mn+n^2 with 0<=m<=n and gcd(m,n)=1 in exactly 2^(n-1) ways. - Chandler

LINKS

Ray Chandler, Table of n, a(n) for n=1..100

FORMULA

a(n) = Prod[i=1..n]A002476(i).

EXAMPLE

a(4) = 53599 = 7 * 13 * 19 * 31.

MATHEMATICA

Rest@FoldList[Times, 1, Select[6 Range[100] + 1, PrimeQ]] (*Chandler*)

CROSSREFS

Cf. A000040, A002476, A002110, A006278, A078586.

Sequence in context: A113372 A131940 A008542 * A177784 A326266 A124557

Adjacent sequences:  A121937 A121938 A121939 * A121941 A121942 A121943

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Sep 03 2006

EXTENSIONS

Extended by Ray Chandler, Oct 01 2007

STATUS

approved

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Last modified July 22 17:01 EDT 2019. Contains 325225 sequences. (Running on oeis4.)