cp's OEIS Frontend

A233451 Numbers k such that k^5 starts with k itself (in base 10).

%I A233451 #27 Sep 12 2024 02:35:13
%S A233451 0,1,10,18,100,178,1000,10000,17783,31623,100000,177828,316228,
%T A233451 1000000,10000000,100000000,1000000000,5623413252,10000000000,
%U A233451 100000000000,177827941004,316227766017,1000000000000,1778279410039,10000000000000,31622776601684
%N A233451 Numbers k such that k^5 starts with k itself (in base 10).
%H A233451 Robert Israel, <a href="/A233451/b233451.txt">Table of n, a(n) for n = 1..1756</a>
%e A233451 18^5 = 1889568 begins with 18, so 18 is in the sequence.
%p A233451 R:= 0,1:
%p A233451 for d from 1 to 100 do
%p A233451   k:= ceil(10^(d/4));
%p A233451   if k^5 - 10^d * k < 10^d then
%p A233451     R:= R, k
%p A233451   fi
%p A233451 od:
%p A233451 R; # _Robert Israel_, Sep 11 2024
%t A233451 kmax=10^6; Select[Range[0,kmax],FromDigits[Drop[IntegerDigits[#^5],-(IntegerLength[#^5]-IntegerLength[#])]]==# &] (* _Stefano Spezia_, Aug 27 2023 *)
%o A233451 (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 A233451 Cf. A052210, A052211, A233452, A233453, A233454, A233455, A233456.
%K A233451 nonn,base,easy
%O A233451 1,3
%A A233451 _Arkadiusz Wesolowski_, Dec 10 2013
%E A233451 0 inserted by _Juhani Heino_, Aug 31 2015