OFFSET
1,1
COMMENTS
a(n) is the smallest prime number p such that floor(p/k) are also primes for all k=1,2,...,n.
This sequence is A078502 - 1. See that entry for more information and further terms. - N. J. A. Sloane, May 04 2009
It is obvious that this sequence is increasing and each term is prime. If n>4 then a(n)==9 (mod 10).
a(n) = -1 (mod 120) for n > 4, see A078502. - Jean-Christophe Hervé, Sep 15 2014
EXAMPLE
Floor(5/2) is prime; floor(11/2) and floor(11/3) are primes; floor(11/2), floor(11/3) and floor(11/4) are primes; floor(7224839/2)...floor(7224839/5) are primes.
a(8)=10780559 because all the eight numbers 10780559,
(10780559-1)/2, (10780559-2)/3, (10780559-3)/4,
(10780559-4)/5, (10780559-5)/6, (10780559-6)/7 and
(10780559-7)/8 are primes and 10780559 is the smallest number m such that (m-k+1)/k is prime for k=1,2,...,8.
PROG
(PARI) isokp(v) = (type(v) == "t_INT") && isprime(v);
a(n) = {if (n==0, return (2)); forprime(p=2, , nb = 0; for (k=1, n, if (! isokp((p-k)/(k+1)), break, nb++); ); if (nb==n, return(p)); ); } \\ Michel Marcus, Sep 15 2014
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Farideh Firoozbakht, Apr 14 2004
EXTENSIONS
Added more terms (from A078502), Joerg Arndt, Sep 15 2014
Edited by N. J. A. Sloane, May 18 2022
STATUS
approved