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
Keywords
Examples
a(2) = 3 + 5 = 8. a(3) = 7 + 11 + 13 + 17 + 19 + 23 = 90.
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.
Crossrefs
Programs
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Mathematica
Table[Plus @@ Table[Prime[i], {i, PrimePi[n!] + 1, PrimePi[(n + 1)!]}], {n, 0, 10}] -
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
Formula
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
Comments