A091825 Integers of the form ((k-1)!*2^(k-1) + 1)/k.

2, 3, 77, 6583, 337808291, 150922350277, 80658585770586353, 88333886984966359579, 204973945587849174028466087, 2822166959135536313284193618131862069, 9187519016643816926988413546511855483871

Offset

0,1

Comments

If p is prime and gcd(q,p)=1 then p divides (p-1)!*q^(p-1) + 1.

Links

Table of n, a(n) for n=0..10.

Example

a(1) = ((1-1)!*2^(1-1) + 1)/1 = 2
((2-1)!*2^(2-1) + 1)/2 = 3/2 is not an integer
a(2) = ((3-1)!*2^(3-1) + 1)/3 = 3

Mathematica

Select[Table[((n-1)! 2^(n-1)+1)/n, {n, 35}], IntegerQ]  (* Harvey P. Dale, Mar 24 2011 *)

Prog

(PARI) for (i=1, 100, if(denominator(((i-1)!*2^(i-1)+1)/i)==1, print(((i-1)!*2^(i-1)+1)/i)));

Crossrefs

Cf. A091824.

Sequence in context: A370988 A371269 A306195 * A166091 A371141 A370993

Adjacent sequences: A091822 A091823 A091824 * A091826 A091827 A091828

Keyword

nonn

Author

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Mar 09 2004

Extensions

Additional term provided by Harvey P. Dale, Mar 24 2011

Status

approved