A294195 -id:A294195 - cp's OEIS frontend

A294194 a(n) is the sum of primes between n!+1 and (n+1)!.

0, 2, 8, 90, 1493, 40148, 1536501, 78716604, 5275720734, 445867194366, 46449459576595, 5844108759723625, 873766735145244948, 153087877536458860660, 31062245895591356844637, 7225340509057562100376047, 1909774727511978452561271489, 569166269815032401548622424344

Offset: 0

Olivier Gérard, Oct 22 2017

nonn

			a(2) = 3 + 5 = 8.
a(3) = 7 + 11 + 13 + 17 + 19 + 23 = 90.

Amiram Eldar, Table of n, a(n) for n = 0..21 (extended using Kim Walisch's primesum; terms 0..19 from Daniel Suteu)
Kim Walisch, primesum program.

Cf. A063959.
Cf. A007504 (sum of first n primes).
Cf. A061232 (number of primes between n!+1 and (n+1)!).
Cf. A294193 (sum of integers between n!+1 and (n+1)!).
Cf. A294195 (product of primes between n!+1 and (n+1)!).

Table[Plus @@ Table[Prime[i], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}], {n, 0, 10}]

a(n) = { my(s = 0); forprime(p=n!+1, (n+1)!, s+=p); s; } \\ Iain Fox, Nov 23 2017

use ntheory ':all'; for(0..100) { print "a($) = ", sum_primes(factorial($)+1, factorial($+1)), "\n"; } # _Daniel Suteu, Nov 15 2018

a(n) = A063959(n+1) - A063959(n). - Amiram Eldar, Jun 14 2024

a(11)-a(13) from Iain Fox, Nov 23 2017
a(14) from Iain Fox, Nov 28 2017
a(15)-a(17) from Daniel Suteu, Nov 15 2018

A294196 Floor of log of product of all primes between n!+1 and (n+1)!.

Original entry on oeis.org

2, 15, 87, 579, 4276, 35103, 322168, 3264471, 36285842, 439070392, 5747983086

Offset: 2

Olivier Gérard, Oct 29 2017

			a(3) = floor(log(7*11*13*17*19*23)) = floor(15.82) = 15.

Cf. A061232 (number of primes between n!+1 and (n+1)!).
Cf. A294194 (sum of primes between n!+1 and (n+1)!).
Cf. A294195 (product of primes between n!+1 and (n+1)!).

Table[Floor[Plus @@ Table[Log[Prime[i]*1.], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}]], {n, 2, 11}]

a(12) from Daniel Suteu, Nov 15 2018

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

Original entry on oeis.org

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

Offset: 2

Olivier Gérard, Oct 29 2017

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

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)!).

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

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

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

a(12) from Jinyuan Wang, Jan 19 2025

cp's OEIS Frontend

A294194 a(n) is the sum of primes between n!+1 and (n+1)!.

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A294196 Floor of log of product of all primes between n!+1 and (n+1)!.

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Extensions

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

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions