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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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3
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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
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OFFSET
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0,11
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COMMENTS
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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
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Nathaniel Johnston, Table of n, a(n) for n = 0..10000
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FORMULA
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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
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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
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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
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f[n_] := If[n == 0, 1, Floor[ Log[10, 10n]]^(Mod[n - 1, 9] + 1)]; Table[ f[n], {n, 0, 73}] (* Robert G. Wilson v, Jan 04 2006 *)
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PROG
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(PARI) apply( A113019(n)=(logint(n+!n, 10)+1)^((n-1)%9+1), [0..99]) \\ M. F. Hasler, Nov 17 2019
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CROSSREFS
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Cf. A101337.
Sequence in context: A251759 A243087 A123464 * A329562 A069877 A085940
Adjacent sequences: A113016 A113017 A113018 * A113020 A113021 A113022
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KEYWORD
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base,easy,nonn
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AUTHOR
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Alexandre Wajnberg, Jan 03 2006
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STATUS
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approved
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