A092023 a(n) is the smallest number m such that m has n distinct prime divisors and if p is a prime divisor of m then p*m - 1 is prime.

2, 6, 30, 420, 32550, 410970, 55137810, 1350063330, 30644204010, 9396949341780, 6805591029957720

Offset

1,1

Comments

2004 has this property, i.e., 2004 = 2^2*3*167, the three numbers 2*2004-1,3*2004-1 and 167*2004-1 are primes. But 2004 is not in the sequence because 2004 is not the smallest number with such property.

Links

Table of n, a(n) for n=1..11.

Carlos Rivera, Puzzle 334. Farideh & the 2004 year, The Prime Puzzles & Problems connection.

Example

a(7) = 55137810 because 55137810 = 2*3*5*7*13*19*1063 and all the seven numbers 2*55137810-1, 3*55137810-1, 5*55137810-1, 7*55137810-1, 13*55137810-1, 19*55137810-1 and 1063*55137810-1 are prime numbers and 55137810 is the smallest number m with such property.

Crossrefs

Cf. A092024.

Cf. A112723, A112724.

Sequence in context: A054934 A001684 A076926 * A112723 A326867 A320830

Adjacent sequences: A092020 A092021 A092022 * A092024 A092025 A092026

Keyword

more,nonn

Author

Farideh Firoozbakht, Feb 18 2004

Extensions

a(10) from Michael S. Branicky, Feb 25 2023

a(11) from Michael S. Branicky, Mar 20 2023

Status

approved