A052211 Numbers k such that k^4 starts with k itself (in base 10).
0, 1, 10, 100, 1000, 10000, 46416, 100000, 464159, 1000000, 2154435, 4641589, 10000000, 21544347, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 2154434690032, 4641588833613, 10000000000000, 21544346900319, 46415888336128
Offset: 1
Examples
46416^4 starts with 46416.
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..500
Programs
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Mathematica
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[ # ]& ] ] ] -
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
Extensions
0 inserted by Juhani Heino, Aug 31 2015