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

Author

Olivier Gérard, Oct 29 2017

Keywords

• nonn
• more

Examples

			a(3) = floor(log(7436429)/log(6)) = floor(8.830...) = 8.
		

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)!).

Programs

Mathematica

Table[Floor[1/Log[n!] Plus @@ Table[Log[Prime[i]*1.], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}]], {n, 2, 10}]

PARI

a(n) = floor(log(vecprod(primes([n!+1, (n+1)!])))/log(n!)); \\ Michel Marcus, Jan 19 2025

Formula

a(n) = Sum_{i=primepi(n!)+1..primepi((n+1)!)} log(prime(i)) / log(n!).

Extensions

a(12) from Jinyuan Wang, Jan 19 2025