A263477 Total number of n-digit positive integers with multiplicative digital root value 2.

1, 8, 68, 466, 2670, 13460, 69420, 417722, 3025242, 21873040, 136901413, 722201372, 3271729383, 13114173697, 48104723380, 167526488628, 574289772576, 1988721563904, 7000834741144, 24759698208450, 86342520209963, 292206955736762, 950480594161453

Offset

1,2

Comments

First differences of A263471.

Links

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

Eric Weisstein's World of Mathematics, Multiplicative Digital Root

Formula

A263476(n) + A000012(n) + a(n) + A000027(n) + A263478(n) + A263479(n) + A263480(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).

Mathematica

Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 2 &] (* 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) == 2, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034049, A051813, A263471.

Sequence in context: A050841 A208947 A296670 * A249390 A190510 A282563

Adjacent sequences: A263474 A263475 A263476 * A263478 A263479 A263480

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved