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A100612
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a(n) = (0! + 1! + ... + (p-1)!) mod p, where p = prime(n).
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5
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0, 1, 4, 6, 1, 10, 13, 9, 21, 17, 2, 5, 4, 16, 18, 13, 28, 22, 65, 68, 55, 20, 27, 76, 80, 13, 50, 43, 65, 109, 56, 81, 93, 134, 82, 10, 131, 4, 30, 104, 29, 170, 104, 165, 9, 122, 130, 42, 225, 50, 69, 12, 128, 60, 147, 52, 16, 56, 7, 218, 154, 264, 198, 48, 299, 205, 251, 101
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OFFSET
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1,3
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COMMENTS
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The greedy inverse (indices of first occurrence of 1, 2, 3, ... in the sequence) is 2, 11, 91, 3, 12, 4, 59, -1, 8, 6, -1, 52, 7, 2550, -1, 14, 10, 15, 5461, 22, 9, 18, 205, 141, 4178, -1, 23, 17, 41, 39, -1, 5297, 937, -1, -1, -1, -1, 5248, 213, -1, 90, 48, 28, 4202, -1, 1718, 313, 64, 119, 27, ... where -1 means the number does not exist or is larger than 8000. - R. J. Mathar, Dec 19 2016
a(16728884) = 26; a(62860131) = 35; sent by Milos Tatarevic. - Michel Marcus, May 18 2019
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B44: is a(n)>0 for n>2?
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LINKS
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T. D. Noe, Plot of first 5000 terms (The red line gives prime(n). There are very few duplicate values in the sequence; the 5000 terms have 4476 values.)
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FORMULA
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MAPLE
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lf:=n->add(k!, k=0..n-1);
[seq(lf(ithprime(n)) mod ithprime(n), n=1..100)];
# 2nd program:
local p, f, a, k;
f := 1 ;
a := 0 ;
p := ithprime(n) ;
for k from 0 to p-1 do
a := modp(a+f, p) ;
f := modp(f*(k+1), p) ;
end do:
a ;
end proc:
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MATHEMATICA
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Table[Mod[Total[Range[0, n-1]!], n], {n, Prime[Range[70]]}] (* Harvey P. Dale, May 06 2013 *)
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PROG
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(PARI) a(n) = {my(p = prime(n), v = vector(p-1, k, Mod(k, p))); for (k=2, p-1, v[k] *= v[k-1]; ); lift(1+vecsum(v)); } \\ Michel Marcus, May 05 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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