A263481 Total number of n-digit positive integers with multiplicative digital root value 8.

1, 22, 138, 889, 4921, 26687, 154539, 870270, 4437621, 20367762, 86589471, 388661761, 2366418106, 18602433227, 142978182070, 952075901928, 5434361620523, 27064481351856, 120477919973804, 497320625548529, 2051776298637086, 9590295679377844, 54933121828772931

Offset

1,2

Comments

First differences of A263475.

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50

Formula

A263476(n) + A000012(n) + A263477(n) + A000027(n) + A263478(n) + A263479(n) + A263480(n) + A000027(n) + a(n) + A000217(n) = A052268(n).

Mathematica

Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 8 &] (* Michael De Vlieger, Oct 21 2015 *)

Prog

(PARI) t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}
a(n) = sum(i=10^(n-1), 10^n - 1, if(t(i) == 8, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034055, A263475.

Sequence in context: A041936 A254699 A183909 * A238170 A275799 A185397

Adjacent sequences: A263478 A263479 A263480 * A263482 A263483 A263484

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

a(9)-a(23) from Hiroaki Yamanouchi, Oct 25 2015

Status

approved