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

1,1

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

Links

Table of n, a(n) for n=1..37.

Example

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

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 *)

Prog

(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(T<T=bitor(T, 2^lift(m^n+=1)), ); S=bitor(S, T)); vecextract([0..99], 2^100-S-1) \\ Slightly faster. - M. F. Hasler, Dec 13 2018

Crossrefs

Sequence in context: A007674 A086719 A115200 * A368045 A191748 A102212

Adjacent sequences: A075820 A075821 A075822 * A075824 A075825 A075826

Keyword

fini,full,easy,nonn,base

Author

Zak Seidov, Oct 14 2002

Extensions

Edited and confirmed by Nathaniel Johnston, Jun 22 2011

Status

approved