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

0,2

Links

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.

Formula

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

Example

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

Mathematica

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

Prog

(PARI) a(n) = { my(s = 0); forprime(p=n!+1, (n+1)!, s+=p); s; } \\ Iain Fox, Nov 23 2017
(Perl) use ntheory ':all'; for(0..100) { print "a($_) = ", sum_primes(factorial($_)+1, factorial($_+1)), "\n"; } # Daniel Suteu, Nov 15 2018

Crossrefs

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)!).

Sequence in context: A153887 A131349 A319124 * A067964 A102895 A372949

Adjacent sequences: A294191 A294192 A294193 * A294195 A294196 A294197

Keyword

nonn

Author

Olivier Gérard, Oct 22 2017

Extensions

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

Status

approved