OFFSET
0,2
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), pp. 117-122.
FORMULA
a(n) = A190121(10^n).
It seems that a(n)/10^(2n-1) -> 3.865783... as n -> oo.
Note: A190121 ~ 0.374... * n^2 [Barbeau]. - Giorgio Balzarotti, Oct 15 2013
a(n) ~ 0.386578334524897563932183729927 * 100^n. - Hiroaki Yamanouchi, Jul 09 2014
The constant is (1/2) * Sum_{p prime} 1/(p*(p-1)) = A136141 / 2 = 0.3865783345... . This constant was given by Barbeau (1961) but with the wrong value 0.374. - Amiram Eldar, Oct 06 2023
PROG
(PARI) s=0; for(k=0, 8, for(n=10^(k-1)+1, 10^k, s+=A003415(n)); print1(s", ")); s
CROSSREFS
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