A263474 Total number of positive integers < 10^n with multiplicative digital root value 6.

1, 14, 155, 1172, 6843, 43538, 318457, 2223803, 14185700, 84670477, 477808607, 2577052118, 13759255632, 75251167843, 418157757456, 2267313716636, 11616142299625, 55909713312571, 257522103127082, 1182251998919171, 5791219719115580, 32715779086392723

Offset

1,2

Comments

Partial sums of A263480.

Links

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

Formula

A263470(n) + A000027(n) + A263471(n) + A000217(n) + A263472(n) + A263473(n) + a(n) + A000217(n) + A263475(n) + A000292(n) = A002283(n).

Mathematica

lim = 6; t = Select[Range[1, 10^lim - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 6 &]; 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) == 6, 1, 0)); \\ Altug Alkan, Oct 19 2015

Crossrefs

Cf. A031347, A034053, A263480.

Sequence in context: A004986 A154248 A006865 * A154347 A001707 A078999

Adjacent sequences: A263471 A263472 A263473 * A263475 A263476 A263477

Keyword

nonn,base

Author

Martin Renner, Oct 19 2015

Extensions

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

Status

approved