

A093553


a(n) is the smallest number m such that (m+k1)/k is prime for k=1,2,...,n.


4



2, 3, 13, 12721, 19441, 5516281, 5516281, 7321991041, 363500177041, 2394196081201, 3163427380990801, 22755817971366481, 3788978012188649281, 2918756139031688155201
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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).
a(n)=1 (mod 120) for all n > 3 (see A163573).  JeanChristophe Hervé, Sep 14 2014
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 (p1)/2, (p2)/3 and (p3)/4 are also prime, and many other properties.  JeanChristophe Hervé, Sep 14 2014


LINKS

Table of n, a(n) for n=1..14.
Walter Nissen, Calculation without Words : Doric Columns of Primes, Up for the Count !


EXAMPLE

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+k1)/k is prime for k=1,2,...,9.


CROSSREFS

Cf. A072875.
Sequence in context: A062648 A094003 A119987 * A253575 A027673 A306039
Adjacent sequences: A093550 A093551 A093552 * A093554 A093555 A093556


KEYWORD

nonn


AUTHOR

Farideh Firoozbakht, Apr 14 2004


STATUS

approved



