This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A093554 #20 Jun 22 2025 16:28:49
%S A093554 2,5,11,11,174599,7224839,10780559,10780559,1086338816639,
%T A093554 50060257410239,7720634052774719,227457297898150319,
%U A093554 7272877497848202239,7272877497848202239
%N A093554 a(n) is the smallest number m such that (m-k+1)/k is prime for k=1,2,...,n.
%C A093554 a(n) is the smallest prime number p such that floor(p/k) are also primes for all k=1,2,...,n.
%C A093554 This sequence is A078502 - 1. See that entry for more information and further terms. - _N. J. A. Sloane_, May 04 2009
%C A093554 It is obvious that this sequence is increasing and each term is prime. If n>4 then a(n)==9 (mod 10).
%C A093554 a(n) = -1 (mod 120) for n > 4, see A078502. - _Jean-Christophe Hervé_, Sep 15 2014
%e A093554 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 A093554 a(8)=10780559 because all the eight numbers 10780559, (10780559-1)/2, (10780559-2)/3, (10780559-3)/4, (10780559-4)/5, (10780559-5)/6, (10780559-6)/7 and (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 A093554 (PARI) isokp(v) = (type(v) == "t_INT") && isprime(v);
%o A093554 a(n) = {if (n==1, return (2)); forprime(p=2, , nb = 0; for (k=1, n-1, if (! isokp((p-k)/(k+1)), break, nb++); ); if (nb==n-1, return(p)); ); } \\ _Michel Marcus_, Sep 15 2014; Jun 22 2025
%Y A093554 Cf. A093553, A181680.
%K A093554 more,nonn
%O A093554 1,1
%A A093554 _Farideh Firoozbakht_, Apr 14 2004
%E A093554 Added more terms (from A078502), _Joerg Arndt_, Sep 15 2014
%E A093554 Edited by _N. J. A. Sloane_, May 18 2022