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

Author

Henry Bottomley, Nov 25 2004

Keywords

• nonn
• easy

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.

Examples

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

Links

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

Crossrefs

Cf. A010809, A051126, A075821.

Programs

Magma

[n^21 mod 100: n in [0..1000]]; // Vincenzo Librandi, Apr 21 2011

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 *)

PARI

a(n)=n^21%100 \\ Charles R Greathouse IV, Apr 06 2016

Formula

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