VOOZH about

URL: https://oeis.org/A294197

⇱ A294197 - OEIS

login
A294197
Floor of log base n! of product of all primes between n!+1 and (n+1)!.
0
3, 8, 27, 120, 650, 4117, 30380, 255000, 2402333, 25086428, 287582999
OFFSET
2,1
FORMULA
a(n) = Sum_{i=primepi(n!)+1..primepi((n+1)!)} log(prime(i)) / log(n!).
EXAMPLE
a(3) = floor(log(7436429)/log(6)) = floor(8.830...) = 8.
MATHEMATICA
Table[Floor[1/Log[n!] Plus @@ Table[Log[Prime[i]*1.], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}]], {n, 2, 10}]
PROG
(PARI) a(n) = logint(vecprod(primes([n!+1, (n+1)!])), n!); \\ Michel Marcus, Jan 19 2025
CROSSREFS
Cf. A061232 (number of primes between n!+1 and (n+1)!).
Cf. A294195 (product of primes between n!+1 and (n+1)!).
Cf. A294196 (log of product of primes between n!+1 and (n+1)!).
Sequence in context: A110886 A104854 A226061 * A030495 A074271 A005641
KEYWORD
nonn,more
AUTHOR
Olivier Gérard, Oct 29 2017
EXTENSIONS
a(12) from Jinyuan Wang, Jan 19 2025
STATUS
approved