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

1,2

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

Formula

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

Mathematica

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

Crossrefs

Cf. A031347, A034049, A051822, A263477.

Sequence in context: A075608 A330630 A282327 * A266125 A290708 A126631

Adjacent sequences: A263468 A263469 A263470 * A263472 A263473 A263474

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

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

Status

approved