A275111 a(n) = prime(n)! mod prime(n+1).
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
Offset: 1
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[Mod[#!, NextPrime@ #] &@ Prime@ n, {n, 120}] (* Michael De Vlieger, Jul 17 2016 *) -
PARI
a(n) = prime(n)! % prime(n+1); \\ Michel Marcus, Jul 17 2016
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PARI
a(n,p=prime(n))=my(q=nextprime(p+1)); if(p==2, 2, lift( 1/prod(r=p+1,q-2, Mod(r,q)) ) ); \\ Charles R Greathouse IV, Jul 18 2016; corrected by Max Alekseyev, May 03 2017
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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
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Python
from sympy import prime from sympy.core.numbers import igcdex def A275111(n): p, q = prime(n), prime(n+1) a = q-1 for i in range(p+1,q): a = (a*igcdex(i,q)[0]) % q return a # Chai Wah Wu, Jul 18 2016
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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
Formula
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
For n>1, a(n) = 1/(prime(n+1)-prime(n)-1)! mod prime(n+1) = 1/(A001223(n)-1)! mod A000040(n+1). - Max Alekseyev, May 03 2017
Extensions
More terms from Altug Alkan, Jul 17 2016
Comments