OFFSET
1,1
COMMENTS
A007489(n) = Sum_{k=1..m} k! = (!(n+1) - 1) = A003422(n+1) - 1 = {0, 1, 3, 9, 33, 153, 873, 5913, 46233, 409113, 4037913, ...}. A007489(n) is divisible by 99 for n=8 and n>9. Corresponding primes of the form (!(n+1) - 1)/99 are {467, 40787, 443987, 225498914387, 11895484822660898387, 2771826449193354891007108898387, 3072603482270933019578343003268898387, ...}.
LINKS
Hisanori Mishima, Factorizations of many number sequences.
Eric Weisstein's World of Mathematics, Left Factorial.
MATHEMATICA
f=0; Do[f=f+n!; If[PrimeQ[f/99], Print[{n, f/99}]], {n, 1, 534}]
Position[Accumulate[Range[1000]!]/99, _?PrimeQ]//Flatten (* The program generates the first 23 terms of the sequence. *) (* Harvey P. Dale, Sep 21 2023 *)
PROG
(Python)
from math import factorial
from sympy import isprime, prime
def afind(limit, startk=8):
if startk <= 8 <= limit: print(8, end=", ")
f, s, startk = 1, 0, max(startk, 10)
for i in range(1, startk):
f *= i
s += f
for k in range(startk, limit+1):
f *= k
s += f
if isprime(s//99):
print(k, end=", ")
afind(535) # Michael S. Branicky, Jan 17 2022
CROSSREFS
KEYWORD
hard,more,nonn
AUTHOR
Alexander Adamchuk, Oct 28 2006
EXTENSIONS
a(21)-a(26) from Michael S. Branicky, Jan 17 2022
a(27) from Michael S. Branicky, Apr 05 2023
STATUS
approved