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A275111
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a(n) = prime(n)! mod prime(n+1).
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5
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2, 1, 1, 2, 1, 3, 1, 4, 22, 1, 33, 7, 1, 8, 19, 30, 1, 43, 12, 1, 27, 14, 23, 24, 17, 1, 18, 1, 19, 19, 22, 8, 1, 94, 1, 140, 72, 28, 62, 91, 1, 105, 1, 33, 1, 177, 97, 38, 1, 39, 2, 1, 19, 15, 160, 204, 1, 247, 47, 1, 291, 299, 52, 1, 53, 198, 132, 55, 1, 59, 3, 176
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OFFSET
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1,1
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COMMENTS
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By Wilson's theorem, if prime(n+1) - prime(n) = 2 then a(n) = 1.
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LINKS
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FORMULA
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For n>1, a(n) = 1/((prime(n)+1)*(prime(n)+2)*...*(prime(n+1)-2)) mod prime(n+1). - Robert Israel, Jul 17 2016; corrected by Max Alekseyev, May 03 2017
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MATHEMATICA
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PROG
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(PARI) a(n) = prime(n)! % prime(n+1); \\ Michel Marcus, Jul 17 2016
(PARI) a(n, p=prime(n)) = my(q=nextprime(p+1)); if(p==2, 2, (1/(q-p-1)!)%q); \\ Max Alekseyev, May 03 2017
(Python)
from sympy import prime
from sympy.core.numbers import igcdex
p, q = prime(n), prime(n+1)
a = q-1
for i in range(p+1, q):
a = (a*igcdex(i, q)[0]) % q
(Python)
from functools import reduce
from sympy import prime
def A275111(n): return ((q:=prime(n+1))-1)*pow(reduce(lambda i, j:i*j%q, range(prime(n)+1, q), 1), -1, q)%q # Chai Wah Wu, Feb 24 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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