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

Offset

0,2

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,1).

Formula

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

G.f.: (1 + 9*x + 81*x^2 + 29*x^3 + 61*x^4 + 49*x^5 + 41*x^6 + 69*x^7 + 21*x^8 + 89*x^9)/(1 - x^10). - Andrew Howroyd, Nov 02 2025

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 *)

Prog

(Magma) [Modexp(9, n, 100): n in [0..110]]; // Vincenzo Librandi, Aug 16 2016
(PARI) a(n) = lift(Mod(9, 100)^n); \\ Michel Marcus, Aug 16 2016

Crossrefs

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

Sequence in context: A219664 A107346 A209280 * A008463 A203656 A043087

Adjacent sequences: A014390 A014391 A014392 * A014394 A014395 A014396

Keyword

nonn,base,easy

Author

N. J. A. Sloane

Status

approved