A224746 a(n) = (Product_{d=1..n-1} (2^d-1)) mod (2^n-1).

0, 1, 3, 6, 5, 0, 7, 60, 301, 837, 11, 2835, 13, 11811, 13454, 2040, 17, 179361, 19, 639375, 1082802, 2818719, 23, 12878775, 28142451, 44845725, 131853841, 161290635, 29, 911545173, 31, 1048560, 4862374202, 11455474329, 26924001270, 62380858995, 37

Offset

1,3

Comments

E. Vantieghem proved that a(n) = n if and only if n is an odd prime (see link).

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

E. Vantieghem, On a congruence only holding for primes, Indagationes Mathematicae, Volume 2, Issue 2, 17 June 1991, pp. 253-255.

Maple

a:= proc(n) local d, m, r; r, m:= 1, 2^n-1;
      for d to n-1 do r:= irem(r*(2^d-1), m) od;
      irem(r, m)
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Apr 17 2013

Mathematica

Table[Mod[Product[2^d-1, {d, 1, n-1}], 2^n-1], {n, 1, 37}] (* Geoffrey Critzer, Sep 28 2013 *)

Prog

(PARI) a(n) = prod(d=1, n-1, 2^d-1) % (2^n-1) \\ Michel Marcus, Apr 17 2013

Crossrefs

Cf. A219732.

Sequence in context: A009782 A294670 A016615 * A296226 A296222 A295999

Adjacent sequences: A224743 A224744 A224745 * A224747 A224748 A224749

Keyword

nonn

Author

Michel Marcus, Apr 17 2013

Status

approved