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A113019
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{Number of digits of n} raised to the power of the {digital root of n}.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32, 64, 128, 256, 512, 2, 4, 8, 16, 32
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,11
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COMMENTS
| n=1 and 32 are fixed points. Are there any others?
First occurrence of k: 1,10,100,11,10000,100000,1000000,12,101,1000000000, ..., . - Robert G. Wilson v.
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..10000
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FORMULA
| a(ijk...) [m digits ijk...] = m^(i+j+k+..[one digit])
a(n)=A055642(n)^A010888(n). - Robert G. Wilson v
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EXAMPLE
| a(0) = 1^0 = 1
a(9) = 1^9 = 1
a(10) = 2^(1+0) = 2
a(89) = 2^(8+9=17=>1+7) = 2^8 = 256
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MAPLE
| A113019 := proc(n) if(n=0)then return 1:fi: return length(n)^(((n-1) mod 9) + 1): end: seq(A113019(n), n=0..100); # Nathaniel Johnston, May 04 2011
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MATHEMATICA
| f[n_] := If[n == 0, 1, Floor[ Log[10, 10n]]^(Mod[n - 1, 9] + 1)]; Table[ f[n], {n, 0, 73}] (from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 04 2006)
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CROSSREFS
| Cf. A101337.
Sequence in context: A104144 A194632 A123464 * A069877 A085940 A061509
Adjacent sequences: A113016 A113017 A113018 * A113020 A113021 A113022
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KEYWORD
| base,easy,nonn
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AUTHOR
| Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Jan 03 2006
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