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A229523
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Partial sum of the arithmetic derivative A003415 (A190121) up to 10^n.
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2
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0, 38, 3906, 386517, 38671110, 3865941752, 386580463478, 38657862140521, 3865783461518530, 386578337105347684, 38657833484501788407, 3865783345588492717623, 386578334529872234861944, 38657833452536035472588254, 3865783345249467526546175599
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OFFSET
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0,2
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COMMENTS
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Note: A190121 ~ 0.374... * n^2 [Barbeau]. - Giorgio Balzarotti, Oct 15 2013
a(n) ~ 0.386578334524897563932183729927 * 100^n. - Hiroaki Yamanouchi, Jul 09 2014
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LINKS
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Hiroaki Yamanouchi, Table of n, a(n) for n = 0..17
E. J. Barbeau, Remark on an arithmetic derivative, Canad. Math. Bull. vol. 4, no. 2, May 1961.
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FORMULA
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a(n) = A190121(10^n).
It seems that a(n)/10^(2n-1) -> 3.865783... as n -> oo.
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PROG
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(PARI) s=0; for(k=0, 8, for(n=10^(k-1)+1, 10^k, s+=A003415(n)); print1(s", ")); s
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CROSSREFS
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Sequence in context: A221111 A322331 A282962 * A173133 A221354 A096558
Adjacent sequences: A229520 A229521 A229522 * A229524 A229525 A229526
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KEYWORD
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nonn,hard
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AUTHOR
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M. F. Hasler, Sep 25 2013
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EXTENSIONS
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a(8)-a(10) from Donovan Johnson, Sep 25 2013
a(11)-a(12) from Giovanni Resta, Mar 13 2014
a(13)-a(14) from Hiroaki Yamanouchi, Jul 09 2014
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STATUS
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approved
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