A263471 - OEIS

%I #28 Oct 25 2015 04:48:39

%S 1,9,77,543,3213,16673,86093,503815,3529057,25402097,162303510,

%T 884504882,4156234265,17270407962,65375131342,232901619970,

%U 807191392546,2795912956450,9796747697594,34556445906044,120898966116007,413105921852769,1363586516014222

%N Total number of positive integers < 10^n with multiplicative digital root value 2.

%C Partial sums of A263477.

%H Hiroaki Yamanouchi, <a href="/A263471/b263471.txt">Table of n, a(n) for n = 1..50</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeDigitalRoot.html">Multiplicative Digital Root</a>

%F A263470(n) + A000027(n) + a(n) + A000217(n) + A263472(n) + A263473(n) + A263474(n) + A000217(n) + A263475(n) + A000292(n) = A002283(n).

%t Length@ Select[Range[10^# - 1], FixedPoint[Times @@ IntegerDigits@ # &, #] == 2 &] & /@ Range@ 6 (* _Michael De Vlieger_, Oct 19 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) == 2, 1, 0)); \\ _Altug Alkan_, Oct 19 2015

%Y Cf. A031347, A034049, A051822, A263477.

%K nonn,base

%O 1,2

%A _Martin Renner_, Oct 19 2015

%E a(8) from _Michael De Vlieger_, Oct 19 2015

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