A263475 Total number of positive integers < 10^n with multiplicative digital root value 8.

1, 23, 161, 1050, 5971, 32658, 187197, 1057467, 5495088, 25862850, 112452321, 501114082, 2867532188, 21469965415, 164448147485, 1116524049413, 6550885669936, 33615367021792, 154093286995596, 651413912544125, 2703190211181211, 12293485890559055

Offset: 1

Author

Martin Renner, Oct 19 2015

Keywords

• nonn
• base

Comments

Partial sums of A263481.

Links

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

Crossrefs

Cf. A031347, A034055, A263481.

Programs

Mathematica

lim = 6; t = Select[Range[1, 10^lim - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 8 &]; Count[t, n_ /; n <= 10^#] & /@ Range@ lim (* Michael De Vlieger, Oct 21 2015 *)

PARI

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

Formula

A263470(n) + A000027(n) + A263471(n) + A000217(n) + A263472(n) + A263473(n) + A263474(n) + A000217(n) + a(n) + A000292(n) = A002283(n).

Extensions

a(9)-a(22) from Hiroaki Yamanouchi, Oct 25 2015