A112723 - OEIS

A112723

a(n) is the smallest number m such that the first n primes is the set of all distinct prime divisors of m and for i=1, 2,...,n prime(i)*m-1 is prime.

2, 6, 30, 420, 2587200, 6787314293760, 52056502538040, 8086849458453393732601350665011200000000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..8.

Carlos Rivera, The Prime Puzzles & Problems connection.

EXAMPLE

a(6) = 6787314293760 because {2,3,5,7,11,13} = {prime(1),prime(2),..., prime(6)} is the set of prime factors of 6787314293760, all six numbers 2*6787314293760-1,3*6787314293760-1, 5*6787314293760-1,7*6787314293760-1,11*6787314293760-1 & 13*6787314293760-1 are prime and 6787314293760 is the first number with such properties.

MATHEMATICA

a[n_] := Block[{p = Prime@Range@n, stp, k}, stp = k = Times @@ p; While[First /@ FactorInteger[k] != p || ! AllTrue[p k - 1, PrimeQ], k += stp]; k]; Array[a, 5] (* Giovanni Resta, Apr 17 2017 *)

CROSSREFS

Cf. A092023, A092024, A112724.

Sequence in context: A001684 A076926 A092023 * A326867 A320830 A074777

Adjacent sequences: A112720 A112721 A112722 * A112724 A112725 A112726

KEYWORD

hard,nonn

AUTHOR

Farideh Firoozbakht, Nov 05 2005

EXTENSIONS

a(7)-a(8) from Giovanni Resta, Apr 14 2017

STATUS

approved