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

1,2

Comments

Partial sums of A263481.

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A031347, A034055, A263481.

Sequence in context: A231216 A133253 A098713 * A214895 A042022 A142091

Adjacent sequences: A263472 A263473 A263474 * A263476 A263477 A263478

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved