A075821 List of possible last two digits (leading zeros omitted) of perfect powers.

0, 1, 3, 4, 7, 8, 9, 11, 12, 13, 16, 17, 19, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 39, 41, 43, 44, 47, 48, 49, 51, 52, 53, 56, 57, 59, 61, 63, 64, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 81, 83, 84, 87, 88, 89, 91, 92, 93, 96, 97, 99

Offset: 1

Author

Zak Seidov, Oct 14 2002

Keywords

• full
• fini
• nonn
• base

Comments

An equivalent definition: Numbers equal to the final two digits of their 21st, 41st, 61st, etc. powers. - Henry Bottomley, Nov 25 2004

Examples

			With leading zeros, the initial terms are 00, 01, 03, 04, 07, 08, 09. Corresponding smallest perfect powers are 100, 2401, 658503, 2304, 16807, 140608, 2209.
1 (01!) is OK because the perfect power 2401=49^2 ends with 01. 9 (09!) is OK because the perfect power 2209=47^2 ends with 09.
11 is in the sequence since 11^21=7400249944258160101211 and the final two digits are 11.
		

Crossrefs

Cf. A010809, A100990.

Formula

Consists of all numbers below 100 except those which are a multiple of 2 but not 4 and those which are a multiple of 5 but not 25. - Henry Bottomley, Nov 25 2004

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 06 2007