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A093553 a(n) is the smallest number m such that (m+k-1)/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). - Jean-Christophe 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 (p-1)/2, (p-2)/3 and (p-3)/4 are also prime, and many other properties. - Jean-Christophe 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+k-1)/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

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Last modified April 24 19:49 EDT 2019. Contains 322446 sequences. (Running on oeis4.)