A219732 a(n) = (Product_{i=1..n-1} (2^i + 1)) modulo (2^n - 1).

0, 0, 1, 0, 1, 9, 1, 0, 74, 33, 1, 1170, 1, 129, 15101, 0, 1, 187758, 1, 67650, 615700, 2049, 1, 4793490, 3247204, 8193, 262658, 4227330, 1, 480000312, 1, 0, 2458463380, 131073, 10787055277, 19903096980, 1, 524289, 67117058, 567489872400, 1, 2686322969514, 1

Offset

1,6

Comments

E. Vantieghem proved that a(n) = 1 if and only if n is an odd prime. - Michel Marcus, Nov 26 2012

Links

Table of n, a(n) for n=1..43.

E. Vantieghem, On a congruence only holding for primes II, arXiv:0812.2841 [math.NT], 2008-2009.

Formula

a(n) = A028362(n) modulo (2^n - 1).

Mathematica

Join[{0}, Table[m = 2^n - 1; prod = 1; Do[prod = Mod[prod*(2^i + 1), m], {i, n - 1}]; prod, {n, 2, 40}]] (* T. D. Noe, Nov 27 2012 *)

Prog

(PARI) a(m) = {for (n=1, m, print1(prod(j=1, n-1, 2^j+1) % (2^n - 1), ", "); ); }
(PARI) a(n)=if(n>2, my(m=2^n-1); lift(prod(i=1, n-1, Mod(2, m)^i+1)), 0) \\ Charles R Greathouse IV, Nov 26 2012

Crossrefs

Cf. A028362.

Sequence in context: A020841 A081801 A176522 * A259314 A266557 A010534

Adjacent sequences: A219729 A219730 A219731 * A219733 A219734 A219735

Keyword

nonn

Author

Michel Marcus, Nov 26 2012

Status

approved