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URL: https://oeis.org/A294194

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A294194
a(n) is the sum of primes between n!+1 and (n+1)!.
4
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
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