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

1,2

Comments

Partial sums of A263478.

Links

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

Formula

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

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 *)

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) == 4, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034051, A263478.

Sequence in context: A255245 A210369 A058920 * A250287 A059598 A327388

Adjacent sequences: A263469 A263470 A263471 * A263473 A263474 A263475

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved