OFFSET
1,3
COMMENTS
a(n) is half the difference between the middle two divisors of A070826(n + 1). - David A. Corneth, Jan 17 2022
LINKS
Jon E. Schoenfield, Table of n, a(n) for n = 1..42
EXAMPLE
a(4)=1 because the product of the first 4 odd primes, 3*5*7*11 = 1155, is 34^2 - 1. a(5)=19 because 15015=3*5*7*11*13=124^2-19^2, and no positive integer less than 19 will work in this situation.
PROG
(PARI) a(n) = my(k=1, p=prod(k=2, n+1, prime(k))); while (!issquare(k^2+p), k++); k; \\ Michel Marcus, Jan 10 2022
(Python)
from math import isqrt
from sympy import primorial, divisors
def A349708(n):
m = primorial(n+1)//2
a = isqrt(m)
d = max(filter(lambda d: d <= a, divisors(m, generator=True)))
return (m//d-d)//2 # Chai Wah Wu, Mar 29 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Peterson, Dec 31 2021
EXTENSIONS
a(15)-a(26) and corrections to a(9) and a(11) from Jinyuan Wang, Jan 07 2022
a(27)-a(30) from Jon E. Schoenfield, Jan 16 2022
STATUS
approved