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A114323
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Largest number whose 5th power has n digits.
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1
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1, 2, 3, 6, 9, 15, 25, 39, 63, 99, 158, 251, 398, 630, 999, 1584, 2511, 3981, 6309, 9999, 15848, 25118, 39810, 63095, 99999, 158489, 251188, 398107, 630957, 999999, 1584893, 2511886, 3981071, 6309573, 9999999, 15848931, 25118864, 39810717
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OFFSET
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1,2
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COMMENTS
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Note that the rightmost digit of n and n^5 are identical. This is to 5th powers as A061439 is to cubes and A049416 is to squares.
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LINKS
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FORMULA
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a(n) = ceiling((10^n)^(1/5)) - 1.
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EXAMPLE
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a(3) = 3 because 3^5 = 243 which has 3 digits, while 4^5 = 1024 has 3 digits.
a(32) = 2511886 because 2511886^5 = 99999914106500508412371346814176 has 32 digits, while 2511887^5 = 100000113160107495177704749808207 has 33 digits.
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MAPLE
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seq(print(n, floor((10^n-1)^(1/5))), n=1..300); # Georg Fischer Apr 17 2024
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MATHEMATICA
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Table[Floor[(10^n-1)^(1/5)], {n, 40}] (* Harvey P. Dale, Dec 10 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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