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%I #22 Aug 27 2023 16:40:02
%S 0,1,6,10,13,36,60,100,1000,10000,100000,129155,278256,1000000,
%T 10000000,21544347,100000000,1000000000,10000000000,59948425032,
%U 100000000000,599484250319,1000000000000,10000000000000,100000000000000,464158883361278,1000000000000000
%N Numbers k such that k^10 starts with k itself (in base 10).
%e 6^10 = 60466176 begins with 6, so 6 is in the sequence.
%t kmax=10^6; Select[Range[0,kmax],FromDigits[Drop[IntegerDigits[#^10],-(IntegerLength[#^10]-IntegerLength[#])]]==# &] (* _Stefano Spezia_, Aug 27 2023 *)
%o (PARI) r=135; print1(1, ", "); e=10; 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, A233454, A233455.
%K nonn,base,easy
%O 1,3
%A _Arkadiusz Wesolowski_, Dec 10 2013
%E 0 inserted by _Juhani Heino_, Aug 31 2015