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%I #29 May 14 2023 23:48:09
%S 2,3,13,12721,19441,5516281,5516281,7321991041,363500177041,
%T 2394196081201,3163427380990801,22755817971366481,3788978012188649281,
%U 2918756139031688155201
%N a(n) is the smallest number m such that (m+k-1)/k is prime for k=1,2,...,n.
%C This sequence is A074200(n) + 1. See that entry for more information. - _N. J. A. Sloane_, May 04 2009
%C It is obvious that this sequence is increasing and each term is prime. If n > 3 then a(n) == 1 (mod 10).
%C From _Jean-Christophe Hervé_, Sep 14 2014: (Start)
%C a(n) == 1 (mod 120) for all n > 3 (see A163573).
%C 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)
%H Walter Nissen, <a href="http://upforthecount.com/math/pdor.html">Calculation without Words : Doric Columns of Primes</a>, Up for the Count !
%e a(9)=363500177041 because all the nine numbers 363500177041,
%e (363500177041+1)/2, (363500177041+2)/3, (363500177041+3)/4,
%e (363500177041+4)/5, (363500177041+5)/6, (363500177041+6)/7,
%e (363500177041+7)/8 and (363500177041+8)/9 are primes and
%e 363500177041 is the smallest number m such that (m+k-1)/k is prime for k=1,2,...,9.
%Y Cf. A072875.
%K nonn,more
%O 1,1
%A _Farideh Firoozbakht_, Apr 14 2004
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