A263480 Total number of n-digit positive integers with multiplicative digital root value 6.

1, 13, 141, 1017, 5671, 36695, 274919, 1905346, 11961897, 70484777, 393138130, 2099243511, 11182203514, 61491912211, 342906589613, 1849155959180, 9348828582989, 44293571012946, 201612389814511, 924729895792089, 4608967720196409, 26924559367277143

Offset

1,2

Comments

First differences of A263474.

Links

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

Formula

A263476(n) + A000012(n) + A263477(n) + A000027(n) + A263478(n) + A263479(n) + a(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).

Mathematica

Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 6 &] (* 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) == 6, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034053, A263474.

Sequence in context: A051639 A138931 A157160 * A210766 A045742 A122011

Adjacent sequences: A263477 A263478 A263479 * A263481 A263482 A263483

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved