%I #22 Aug 27 2023 16:24:06
%S 0,1,4,10,16,40,100,631,1000,1585,2512,10000,15849,25119,100000,
%T 1000000,10000000,15848932,100000000,1000000000,6309573445,
%U 10000000000,100000000000,251188643151,1000000000000,3981071705535,6309573444802,10000000000000
%N Numbers k such that k^6 starts with k itself (in base 10).
%e 4^6 = 4096 begins with 4, so 4 is in the sequence.
%t kmax=10^6; Select[Range[0,kmax],FromDigits[Drop[IntegerDigits[#^6],-(IntegerLength[#^6]-IntegerLength[#])]]==# &] (* _Stefano Spezia_, Aug 27 2023 *)
%o (PARI) r=65; print1(1, ", "); e=6; 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, A233453, A233454, A233455, A233456.
%K nonn,base,easy
%O 1,3
%A _Arkadiusz Wesolowski_, Dec 10 2013
%E 0 inserted by _Juhani Heino_, Aug 31 2015
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