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%I #30 Aug 27 2023 16:39:08
%S 0,1,10,100,1000,10000,46416,100000,464159,1000000,2154435,4641589,
%T 10000000,21544347,100000000,1000000000,10000000000,100000000000,
%U 1000000000000,2154434690032,4641588833613,10000000000000,21544346900319,46415888336128
%N Numbers k such that k^4 starts with k itself (in base 10).
%H Andrew Howroyd, <a href="/A052211/b052211.txt">Table of n, a(n) for n = 1..500</a>
%e 46416^4 starts with 46416.
%t Join[{0}, Sort[ Table[ 10^i,{i,0,22} ]~Join~Select[ Table[ Ceiling[ 10.^(1/3)*10^i ],{i,0,22} ], Take[ IntegerDigits[ #^4 ],Length[ IntegerDigits[ # ] ] ]==IntegerDigits[ # ]& ]~Join~Select[ Table[ Ceiling[ 10.^(2/3)*10^i ],{i,0,22} ],Take[ IntegerDigits[ #^4 ],Length[ IntegerDigits[ # ] ] ]==IntegerDigits[ # ]& ] ] ]
%o (PARI) r=41; print1(1, ", "); e=4; 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, ", "))); \\ _Arkadiusz Wesolowski_, Dec 10 2013
%Y Cf. A052210, A233451, A233452, A233453, A233454, A233455, A233456.
%K nonn,base,easy
%O 1,3
%A _Erich Friedman_, Jan 29 2000
%E 0 inserted by _Juhani Heino_, Aug 31 2015
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