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

1,1

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)

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Different from A092965 (see Comments).

Sequence in context: A104365 A104372 A092969 * A092965 A051454 A051452

Adjacent sequences: A089133 A089134 A089135 * A089137 A089138 A089139

Keyword

easy,nonn

Author

Cino Hilliard, Dec 05 2003

Status

approved