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Search: id:A066022
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| A066022 |
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Number of digits in n^n. |
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+0
2
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| 1, 1, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 15, 17, 18, 20, 21, 23, 25, 27, 28, 30, 32, 34, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 88, 90, 92, 94, 96, 98, 101, 103, 105, 107, 109, 112, 114, 116, 118, 121, 123, 125
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This is almost certainly the same as the number of decimal digits of the sum of the n-th powers of the divisors of n (a sequence submitted by Labos E. (labos(AT)ana.sote.hu) on Jan 14 2002). Although no formal proof for this is known, Jon Schoenfield has verified it for n up to 10^8 and has given a plausible heuristic argument that it is true for all n.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
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a(n) = floor(n*log(n)/log(10)) + 1. Not correct in PARI for n=100, n=1000, ... . See my PARI program.
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MAPLE
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[seq(length(n^n), n=1..55)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 10 2007
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MATHEMATICA
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Table[Length[IntegerDigits[DivisorSigma[w, w]]], {w, 1, 100}] - Labos E. (labos(AT)ana.sote.hu), Jan 14 2002
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PROGRAM
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(PARI) digitsIn(x)= { local(d); if (x==0, return(1)); d=1 + log(x)\log(10); if (10^d == x, d++, if (10^(d-1) > x, d--)); return(d) } { for (n=1, 1000, a=digitsIn(n^n); write("b066022.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 07 2009]
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CROSSREFS
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Cf. A034886
Sequence in context: A039206 A039118 A067314 this_sequence A052047 A078831 A031177
Adjacent sequences: A066019 A066020 A066021 this_sequence A066023 A066024 A066025
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KEYWORD
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base,easy,nonn,new
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AUTHOR
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Robert A. Stump (bee_ess107(AT)yahoo.com), Dec 11 2001
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com) Jan 03 2009 at the suggestion of Jon Schoenfield.
Comment added to FORMULA and OFFSET changed from 0,3 to 1,3 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Nov 07 2009
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