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A052211 Numbers n such that n^4 starts with n itself (in base 10). 9
0, 1, 10, 100, 1000, 10000, 46416, 100000, 464159, 1000000, 2154435, 4641589, 10000000, 21544347, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 2154434690032, 4641588833613, 10000000000000, 21544346900319, 46415888336128 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

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

EXAMPLE

46416^4 starts with 46416.

MATHEMATICA

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

STATUS

approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)