A075823 Numbers that are not the last two digits (leading zeros omitted) of any perfect power.

2, 5, 6, 10, 14, 15, 18, 20, 22, 26, 30, 34, 35, 38, 40, 42, 45, 46, 50, 54, 55, 58, 60, 62, 65, 66, 70, 74, 78, 80, 82, 85, 86, 90, 94, 95, 98

Offset: 1

Author

Zak Seidov, Oct 14 2002

Keywords

• fini
• full
• easy
• nonn
• base

Comments

With leading zeros, the initial terms are 02, 05, 06.

To compute the sequence, it is sufficient to consider the residue mod 100 of powers of numbers < 100 until the same value is reached for the second time. - M. F. Hasler, Dec 13 2018

Examples

			9 (09!) not in the list because the perfect power 2209 = 47^2 ends with 09.
		

Programs

Maple

s:={$(0..99)}: for b from 0 to 99 do for p from 2 to 101 do s:=s minus {b^p mod 100}: od: od: op(s); # Nathaniel Johnston, Jun 22 2011

Mathematica

S=Range[2,99]; Do[n=1; T={}; While[T != (T = Union[T, {PowerMod[k, ++n, 100]}]), S=Complement[S,T]], {k,2,99}]; S (* Amiram Eldar, Dec 13 2018 after M. F. Hasler's pari code *)

PARI

S=[2..99]; for(k=2,99,my(m=Mod(k,100),n=1,T=[]);while(T!=T=setunion(T,[m^n+=1]),); S=setminus(S,lift(T)));S \\ Slightly shorter. - M. F. Hasler, Dec 13 2018

PARI

S=0;for(k=2,99,my(m=Mod(k,100),n=1,T=0);while(TM. F. Hasler, Dec 13 2018

Extensions

Edited and confirmed by Nathaniel Johnston, Jun 22 2011