A263471 Total number of positive integers < 10^n with multiplicative digital root value 2.

1, 9, 77, 543, 3213, 16673, 86093, 503815, 3529057, 25402097, 162303510, 884504882, 4156234265, 17270407962, 65375131342, 232901619970, 807191392546, 2795912956450, 9796747697594, 34556445906044, 120898966116007, 413105921852769, 1363586516014222

Offset: 1

Author

Martin Renner, Oct 19 2015

Keywords

• nonn
• base

Comments

Partial sums of A263477.

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50
• Eric Weisstein's World of Mathematics, Multiplicative Digital Root

Crossrefs

Cf. A031347, A034049, A051822, A263477.

Programs

Mathematica

Length@ Select[Range[10^# - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 2 &] & /@ Range@ 6 (* Michael De Vlieger, Oct 19 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) == 2, 1, 0)); \\ Altug Alkan, Oct 19 2015

Formula

A263470(n) + A000027(n) + a(n) + A000217(n) + A263472(n) + A263473(n) + A263474(n) + A000217(n) + A263475(n) + A000292(n) = A002283(n).

Extensions

a(8) from Michael De Vlieger, Oct 19 2015

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