A100990 a(n) = n^21 mod 100.

0, 1, 52, 3, 4, 25, 56, 7, 8, 9, 0, 11, 12, 13, 64, 75, 16, 17, 68, 19, 0, 21, 72, 23, 24, 25, 76, 27, 28, 29, 0, 31, 32, 33, 84, 75, 36, 37, 88, 39, 0, 41, 92, 43, 44, 25, 96, 47, 48, 49, 0, 51, 52, 53, 4, 75, 56, 57, 8, 59, 0, 61, 12, 63, 64, 25, 16, 67, 68, 69, 0, 71, 72, 73, 24

Offset

0,3

Comments

Also n^(20k+1) mod 100 for any positive integer k.

There are 63 numbers (A075821) where the final two digits of n^21, n^41, n^61, etc. are equal to n.

Period 100.

Links

Jianing Song, Table of n, a(n) for n = 0..99 (a period)

Formula

a(n) = A051126(A010809(n), 100) = a(n-100).

Example

a(11) = 11 since 11^21 = 7400249944258160101211 and the final two digits are 11.

Mathematica

Table[Mod[n^21, 100], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Apr 13 2011 *)
PowerMod[Range[0, 80], 21, 100] (* Harvey P. Dale, Mar 15 2015 *)

Prog

(Magma) [n^21 mod 100: n in [0..1000]]; // Vincenzo Librandi, Apr 21 2011
(PARI) a(n)=n^21%100 \\ Charles R Greathouse IV, Apr 06 2016

Crossrefs

Cf. A010809, A051126, A075821.

Sequence in context: A022079 A230107 A275412 * A298573 A048365 A317416

Adjacent sequences: A100987 A100988 A100989 * A100991 A100992 A100993

Keyword

nonn,easy

Author

Henry Bottomley, Nov 25 2004

Status

approved