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

1,3

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Example

46416^4 starts with 46416.

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[ # ]& ] ] ]

Prog

(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

Crossrefs

Cf. A052210, A233451, A233452, A233453, A233454, A233455, A233456.

Sequence in context: A219111 A232659 A232660 * A136845 A272503 A136837

Adjacent sequences: A052208 A052209 A052210 * A052212 A052213 A052214

Keyword

nonn,base,easy

Author

Erich Friedman, Jan 29 2000

Extensions

0 inserted by Juhani Heino, Aug 31 2015

Status

approved