A093554 a(n) is the smallest number m such that (m-k+1)/k is prime for k=1,2,...,n.

2, 5, 11, 11, 174599, 7224839, 10780559, 10780559, 1086338816639, 50060257410239, 7720634052774719, 227457297898150319, 7272877497848202239, 7272877497848202239

Offset: 1

Author

Farideh Firoozbakht, Apr 14 2004

Keywords

• more
• nonn

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

Examples

			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.
		

Crossrefs

Cf. A093553, A181680.

Programs

PARI

isokp(v) = (type(v) == "t_INT") && isprime(v);
a(n) = {if (n==1, return (2)); forprime(p=2, , nb = 0; for (k=1, n-1, if (! isokp((p-k)/(k+1)), break, nb++); ); if (nb==n-1, return(p)); ); }  \\ Michel Marcus, Sep 15 2014; Jun 22 2025

Extensions

Added more terms (from A078502), Joerg Arndt, Sep 15 2014

Edited by N. J. A. Sloane, May 18 2022