

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
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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^(n1) 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



