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

1,1

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

Links

Table of n, a(n) for n=1..14.

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

Cf. A093553, A181680.

Sequence in context: A155767 A079782 A371433 * A168453 A136990 A136968

Adjacent sequences: A093551 A093552 A093553 * A093555 A093556 A093557

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