A263472 - OEIS

%I #25 Oct 25 2015 04:49:52

%S 1,10,65,279,894,2345,6174,66354,1005399,9737884,66699415,356586629,

%T 1585685916,6342292785,30560724590,264486626166,2926013859615,

%U 28611339267816,232062904906327,1588966488941437,9421788721876388,49444241961339027,233673191793220620

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

%C Partial sums of A263478.

%H Hiroaki Yamanouchi, <a href="/A263472/b263472.txt">Table of n, a(n) for n = 1..50</a>

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

%t 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 *)

%o (PARI) t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}

%o a(n) = sum(i=1, 10^n - 1, if(t(i) == 4, 1, 0)); \\ _Altug Alkan_, Oct 19 2015

%Y Cf. A031347, A034051, A263478.

%K nonn,base

%O 1,2

%A _Martin Renner_, Oct 19 2015

%E a(9)-a(23) from _Hiroaki Yamanouchi_, Oct 25 2015