A093554 - OEIS

%I #16 May 18 2022 11:44:23

%S 2,5,11,11,174599,7224839,10780559,10780559,1086338816639,

%T 50060257410239,7720634052774719,227457297898150319,

%U 7272877497848202239,7272877497848202239

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

%C a(n) is the smallest prime number p such that floor(p/k) are also primes for all k=1,2,...,n.

%C This sequence is A078502 - 1. See that entry for more information and further terms. - _N. J. A. Sloane_, May 04 2009

%C It is obvious that this sequence is increasing and each term is prime. If n>4 then a(n)==9 (mod 10).

%C a(n) = -1 (mod 120) for n > 4, see A078502. - _Jean-Christophe Hervé_, Sep 15 2014

%e 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.

%e a(8)=10780559 because all the eight numbers 10780559,

%e (10780559-1)/2, (10780559-2)/3, (10780559-3)/4,

%e (10780559-4)/5, (10780559-5)/6, (10780559-6)/7 and

%e (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.

%o (PARI) isokp(v) = (type(v) == "t_INT") && isprime(v);

%o 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

%Y Cf. A093553, A181680.

%K more,nonn

%O 1,1

%A _Farideh Firoozbakht_, Apr 14 2004

%E Added more terms (from A078502), _Joerg Arndt_, Sep 15 2014

%E Edited by _N. J. A. Sloane_, May 18 2022