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

2, 3, 7, 13, 61, 241, 2521, 20161, 72577, 604801, 39916801, 59875201, 3113510401, 17435658241, 186810624001, 10461394944001, 118562476032001, 246245142528001, 24329020081766401, 304112751022080001

Offset: 1

Author

Cino Hilliard, Dec 05 2003

Keywords

• easy
• nonn

Comments

From Martin Fuller, Apr 26 2007: (Start)

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.

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)

Examples

			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
		

Links

• Martin Fuller, Table of n, a(n) for n = 1..200

Crossrefs

Different from A092965 (see Comments).

Programs

Mathematica

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 *)

PARI

nfactp2d2(n,m) = { for(x=1,n, for(k=1,m, y=floor((x!+ k)/k); if(isprime(y),print1(y",");break) ) ) }

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