A260178 a(n) = hyperfactorial(prime(n)-1) mod prime(n).

1, 1, 3, 1, 10, 8, 13, 18, 22, 17, 30, 6, 9, 42, 1, 30, 1, 50, 66, 70, 27, 1, 1, 34, 22, 10, 1, 1, 76, 15, 1, 130, 37, 1, 105, 150, 28, 162, 166, 93, 178, 19, 1, 81, 14, 1, 1, 222, 226, 107, 144, 238, 64, 1, 16, 1, 82, 270, 60, 53, 1, 155, 1, 310, 288, 203, 1

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 687 terms from Matthew Campbell)

Formula

a(n) = A002109(A000040(n)-1) mod A000040(n).

Example

a(2) = hyperfactorial(2) mod 3 = (2^2*1^1) mod 3 = 4 mod 3 = 1.

Maple

a:= proc(n) option remember; local i, p, r, v;
      p, r, v:= ithprime(n), 1$2;
      for i from p-1 to 1 by -1 do
        v:= v*i mod p; r:= r*v mod p
      od; r
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jul 21 2015

Mathematica

Table[Mod[Hyperfactorial[Prime[n] - 1], Prime[n]], {n, 1, 200}]

Prog

(PARI) a(n, p=prime(n))=lift(prod(k=2, p-1, Mod(k, p)^k)) \\ Charles R Greathouse IV, Jul 23 2015

Crossrefs

Cf. A000040, A002109, A260611.

Sequence in context: A052964 A084178 A262030 * A195812 A264491 A144697

Adjacent sequences: A260175 A260176 A260177 * A260179 A260180 A260181

Keyword

nonn,easy

Author

Matthew Campbell, Jul 17 2015

Status

approved