A294197 Floor of log base n! of product of all primes between n!+1 and (n+1)!.

3, 8, 27, 120, 650, 4117, 30380, 255000, 2402333, 25086428, 287582999

Offset

2,1

Links

Table of n, a(n) for n=2..12.

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

Adjacent sequences: A294194 A294195 A294196 * A294198 A294199 A294200

Keyword

nonn,more

Author

Olivier Gérard, Oct 29 2017

Extensions

a(12) from Jinyuan Wang, Jan 19 2025

Status

approved