This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A075823 #15 Dec 14 2018 04:36:49
%S A075823 2,5,6,10,14,15,18,20,22,26,30,34,35,38,40,42,45,46,50,54,55,58,60,62,
%T A075823 65,66,70,74,78,80,82,85,86,90,94,95,98
%N A075823 Numbers that are not the last two digits (leading zeros omitted) of any perfect power.
%C A075823 With leading zeros, the initial terms are 02, 05, 06.
%C A075823 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
%e A075823 9 (09!) not in the list because the perfect power 2209 = 47^2 ends with 09.
%p A075823 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
%t A075823 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 *)
%o A075823 (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
%o A075823 (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
%K A075823 fini,full,easy,nonn,base
%O A075823 1,1
%A A075823 _Zak Seidov_, Oct 14 2002
%E A075823 Edited and confirmed by _Nathaniel Johnston_, Jun 22 2011