A014393 Final 2 digits of 9^n.

1, 9, 81, 29, 61, 49, 41, 69, 21, 89, 1, 9, 81, 29, 61, 49, 41, 69, 21, 89, 1, 9, 81, 29, 61, 49, 41, 69, 21, 89, 1, 9, 81, 29, 61, 49, 41, 69, 21, 89, 1, 9, 81, 29, 61, 49, 41, 69, 21, 89, 1, 9, 81, 29, 61, 49, 41, 69, 21, 89

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Comments

Period is 10, i.e., a(n+10) = a(n). - Martin Renner, Jun 11 2020

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to final digits of numbers

Crossrefs

Cf. A001019 (9^n), A010690 (final digit of 9^n).

Programs

Magma

[Modexp(9, n, 100): n in [0..110]]; // Vincenzo Librandi, Aug 16 2016

Maple

seq(9^n mod 100, n=0..80); # Martin Renner, Jun 11 2020

Mathematica

Flatten[Prepend[FromDigits[Take[IntegerDigits[#],-2]]&/@(9^Range[2,60]),{1,9}]] (* Harvey P. Dale, Jan 22 2011 *)
PowerMod[9, Range[0, 80], 100] (* Vincenzo Librandi, Aug 16 2016 *)

PARI

a(n) = lift(Mod(9, 100)^n); \\ Michel Marcus, Aug 16 2016

Formula

a(n) = 9^n mod 100. - Martin Renner, Jun 11 2020