A227772 Sequence based on factorial representation converging to 1 in 2-adic numbers, and 0 in p-adic numbers for any other p.

0, 1, 3, 9, 105, 225, 945, 36225, 76545, 2253825, 9511425, 89345025, 1526349825, 26434433025, 287969306625, 12057038618625, 179439357722625, 5870438207258625, 37882306735898625, 1984203913277210625, 11715811945983770625, 982443713208463130625, 15594453174317362970625

Offset: 1

Author

Franklin T. Adams-Watters, Jul 30 2013

Keywords

• nonn

Comments

This is an example to show how a sequence can be constructed to converge to an arbitrary p-adic number chosen independently for each p.

Examples

			5! = 2^3 * 3 * 5. Solving for m == 1 (mod 2^3), 0 (mod 3) and 0 (mod 5), we get m == 105 (mod 120), so we take a(5) = 105.
The factorial base representation is ...114111.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A000142, A049606, A060818, A007623.

Programs

PARI

a(n)=lift(chinese(Mod(1,denominator(polcoeff(pollegendre(n), n))),Mod(0,denominator(2^n/n!)))) /* Ralf Stephan, Aug 01 2013 */

Formula

Solve for a(n) == 1 (mod A060818(n)) and a(n) == 0 (mod A049606), taking the least nonnegative residue.

Extensions

More terms from Ralf Stephan, Aug 01 2013

More terms from Jinyuan Wang, Jan 16 2021