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A229523 Partial sum of the arithmetic derivative A003415 (A190121) up to 10^n. 2
0, 38, 3906, 386517, 38671110, 3865941752, 386580463478, 38657862140521, 3865783461518530, 386578337105347684, 38657833484501788407, 3865783345588492717623, 386578334529872234861944, 38657833452536035472588254, 3865783345249467526546175599 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Note: A190121 ~ 0.374... * n^2 [Barbeau]. - Giorgio Balzarotti, Oct 15 2013

a(n) ~ 0.386578334524897563932183729927 * 100^n. - Hiroaki Yamanouchi, Jul 09 2014

LINKS

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.

FORMULA

a(n) = A190121(10^n).

It seems that a(n)/10^(2n-1) -> 3.865783... as n -> oo.

PROG

(PARI) s=0; for(k=0, 8, for(n=10^(k-1)+1, 10^k, s+=A003415(n)); print1(s", ")); s

CROSSREFS

Sequence in context: A221111 A322331 A282962 * A173133 A221354 A096558

Adjacent sequences:  A229520 A229521 A229522 * A229524 A229525 A229526

KEYWORD

nonn,hard

AUTHOR

M. F. Hasler, Sep 25 2013

EXTENSIONS

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

STATUS

approved

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Last modified May 23 07:08 EDT 2019. Contains 323508 sequences. (Running on oeis4.)