OFFSET
0,2
COMMENTS
Erdős and Straus asked if a(n) exists for all n.
LINKS
Thomas Bloom, Problem 389, Erdős Problems.
Erdős problems database contributors, Erdős problem database, see no. 389.
EXAMPLE
3*4*5*6 | 7*8*9*10, so a(2) = 4.
PROG
(PARI) a(n) = my(k=1); while(prod(i=1, k, n+k+i)%prod(i=1, k, n+i), k++); k;
(Python)
from itertools import count
def A375071(n):
a, b = n+1, n+2
for k in count(1):
if not b%a:
return k
a *= n+k+1
b = b*(n+2*k+1)*(n+2*k+2)//(n+k+1) # Chai Wah Wu, Aug 01 2024
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Ralf Stephan, Jul 29 2024
EXTENSIONS
a(10)-a(18) from Bhavik Mehta, Aug 16 2024
STATUS
approved