A093553 a(n) is the smallest number m such that (m+k-1)/k is prime for k=1,2,...,n.

2, 3, 13, 12721, 19441, 5516281, 5516281, 7321991041, 363500177041, 2394196081201, 3163427380990801, 22755817971366481, 3788978012188649281, 2918756139031688155201

Offset: 1

Author

Farideh Firoozbakht, Apr 14 2004

Keywords

• nonn
• more

Comments

This sequence is A074200(n) + 1. See that entry for more information. - N. J. A. Sloane, May 04 2009

It is obvious that this sequence is increasing and each term is prime. If n > 3 then a(n) == 1 (mod 10).

From Jean-Christophe Hervé, Sep 14 2014: (Start)

a(n) == 1 (mod 120) for all n > 3 (see A163573).

a(4) = 12721 is a quite remarkable number: it is a palindromic prime, its 5 (prime) digits sum to 13, still a prime number (and the preceding element in this sequence, among other things), and as the fourth element of this sequence, it is the smallest prime such that (p-1)/2, (p-2)/3 and (p-3)/4 are also prime, and many other properties. (End)

Examples

			a(9)=363500177041 because all the nine numbers 363500177041,
(363500177041+1)/2, (363500177041+2)/3, (363500177041+3)/4,
(363500177041+4)/5, (363500177041+5)/6, (363500177041+6)/7,
(363500177041+7)/8 and (363500177041+8)/9 are primes and
363500177041 is the smallest number m such that (m+k-1)/k is prime for k=1,2,...,9.
		

Links

• Walter Nissen, Calculation without Words : Doric Columns of Primes, Up for the Count !

Crossrefs

Cf. A072875.