cp's OEIS Frontend

A089136 Primes in the progression (n! + m)/m where n advances by 1 and m resets to 1 upon each prime occurrence.

%I A089136 #13 Apr 16 2024 13:50:41
%S A089136 2,3,7,13,61,241,2521,20161,72577,604801,39916801,59875201,3113510401,
%T A089136 17435658241,186810624001,10461394944001,118562476032001,
%U A089136 246245142528001,24329020081766401,304112751022080001
%N A089136 Primes in the progression (n! + m)/m where n advances by 1 and m resets to 1 upon each prime occurrence.
%C A089136 From _Martin Fuller_, Apr 26 2007: (Start)
%C A089136 Both this sequence and A092965 involve the largest prime of the form (n!/m)+1 but they differ in the allowed values of m. The present sequence allows any integer m dividing n!. But A092965 requires m to be the product of distinct numbers up to n.
%C A089136 I believe that the sequences differ at n=104 and n=106: a(104)=(104!/121)+1, A092965(104)=(104!/266)+1, a(106)=(106!/121)+1, A092965(106)=(106!/133)+1. (End)
%H A089136 Martin Fuller, <a href="/A089136/b089136.txt">Table of n, a(n) for n = 1..200</a>
%e A089136 n=7,m=1, (7!+ 1)/1 = 5041 not prime, m advances to 2, (7!+2)/2 = 2521 prime keep it. n advances to 8 and m resets to 1. (8!+ 1)/1 = 61*661 not prime. m advances to 2. (8!+2)/2 = 20161 prime keep it n advances to 9 etc
%t A089136 k = m = 1; Reap[Do[If[PrimeQ[#], k++; m = 1; Sow[#], m++] &[(k! + m)/m], {n, 100}]][[-1, 1]] (* _Michael De Vlieger_, Apr 16 2024 *)
%o A089136 (PARI) nfactp2d2(n,m) = { for(x=1,n, for(k=1,m, y=floor((x!+ k)/k); if(isprime(y),print1(y",");break) ) ) }
%o A089136 (PARI) lista(nn) = my(list = List()); for(x=1, nn, my(k=1, y); while (!isprime(y=floor((x!+ k)/k)), k++); listput(list, y)); Vec(list); \\ _Michel Marcus_, Apr 16 2024
%Y A089136 Different from A092965 (see Comments).
%K A089136 easy,nonn
%O A089136 1,1
%A A089136 _Cino Hilliard_, Dec 05 2003