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

1,3

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.

Links

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

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A000142, A049606, A060818, A007623.

Sequence in context: A018716 A018725 A135989 * A125652 A232701 A364495

Adjacent sequences: A227769 A227770 A227771 * A227773 A227774 A227775

Keyword

nonn

Author

Franklin T. Adams-Watters, Jul 30 2013

Extensions

More terms from Ralf Stephan, Aug 01 2013

More terms from Jinyuan Wang, Jan 16 2021

Status

approved