A263478 Total number of n-digit positive integers with multiplicative digital root value 4.

1, 9, 55, 214, 615, 1451, 3829, 60180, 939045, 8732485, 56961531, 289887214, 1229099287, 4756606869, 24218431805, 233925901576, 2661527233449, 25685325408201, 203451565638511, 1356903584035110, 7832822232934951, 40022453239462639, 184228949831881593

Offset

1,2

Comments

First differences of A263472.

Links

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

Formula

A263476(n) + A000012(n) + A263477(n) + A000027(n) + a(n) + A263479(n) + A263480(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).

Mathematica

Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 4 &] (* 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) == 4, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034051, A263472.

Sequence in context: A299519 A068970 A141530 * A326249 A016269 A005770

Adjacent sequences: A263475 A263476 A263477 * A263479 A263480 A263481

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved