A263472 Total number of positive integers < 10^n with multiplicative digital root value 4.

1, 10, 65, 279, 894, 2345, 6174, 66354, 1005399, 9737884, 66699415, 356586629, 1585685916, 6342292785, 30560724590, 264486626166, 2926013859615, 28611339267816, 232062904906327, 1588966488941437, 9421788721876388, 49444241961339027, 233673191793220620

Offset: 1

Author

Martin Renner, Oct 19 2015

Keywords

• nonn
• base

Comments

Partial sums of A263478.

Links

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

Crossrefs

Cf. A031347, A034051, A263478.

Programs

Mathematica

lim = 6; t = Select[Range[1, 10^lim - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 4 &]; Count[t, n_ /; n <= 10^#] & /@ Range@ lim (* Michael De Vlieger, Oct 21 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) == 4, 1, 0)); \\ Altug Alkan, Oct 19 2015

Formula

A263470(n) + A000027(n) + A263471(n) + A000217(n) + a(n) + A263473(n) + A263474(n) + A000217(n) + A263475(n) + A000292(n) = A002283(n).

Extensions

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