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%I #27 Sep 12 2024 02:35:13
%S 0,1,10,18,100,178,1000,10000,17783,31623,100000,177828,316228,
%T 1000000,10000000,100000000,1000000000,5623413252,10000000000,
%U 100000000000,177827941004,316227766017,1000000000000,1778279410039,10000000000000,31622776601684
%N Numbers k such that k^5 starts with k itself (in base 10).
%H Robert Israel, <a href="/A233451/b233451.txt">Table of n, a(n) for n = 1..1756</a>
%e 18^5 = 1889568 begins with 18, so 18 is in the sequence.
%p R:= 0,1:
%p for d from 1 to 100 do
%p k:= ceil(10^(d/4));
%p if k^5 - 10^d * k < 10^d then
%p R:= R, k
%p fi
%p od:
%p R; # _Robert Israel_, Sep 11 2024
%t kmax=10^6; Select[Range[0,kmax],FromDigits[Drop[IntegerDigits[#^5],-(IntegerLength[#^5]-IntegerLength[#])]]==# &] (* _Stefano Spezia_, Aug 27 2023 *)
%o (PARI) r=54; print1(1, ", "); e=5; 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, A233452, 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