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%I #25 Aug 27 2023 16:23:13
%S 0,1,2,10,14,72,100,139,518,1000,10000,13895,19307,26827,37276,100000,
%T 1000000,10000000,13894955,26826958,100000000,193069773,517947468,
%U 1000000000,1930697729,10000000000,100000000000,268269579528,1000000000000,3727593720315
%N Numbers k such that k^8 starts with k itself (in base 10).
%e 2^8 = 256 begins with 2, so 2 is in the sequence.
%t Join[{0}, Select[Range@ 1000000, Take[IntegerDigits[#^8], IntegerLength@ #] == IntegerDigits@ # &]] (* _Michael De Vlieger_, Aug 31 2015 *)
%o (PARI) r=88; print1(1, ", "); e=8; for(n=2, r, p=round((10^(1/(e-1)))^n); f=p^e; b=10^(#Str(f)-#Str(p)); if((f-lift(Mod(f, b)))/b==p, print1(p, ", ")));
%Y Cf. A052210, A052211, A233451, A233452, A233453, A233455, A233456.
%K nonn,base,easy
%O 1,3
%A _Arkadiusz Wesolowski_, Dec 10 2013
%E 0 inserted by _Juhani Heino_, Aug 31 2015