This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A263477 #32 Feb 16 2025 08:33:27
%S A263477 1,8,68,466,2670,13460,69420,417722,3025242,21873040,136901413,
%T A263477 722201372,3271729383,13114173697,48104723380,167526488628,
%U A263477 574289772576,1988721563904,7000834741144,24759698208450,86342520209963,292206955736762,950480594161453
%N A263477 Total number of n-digit positive integers with multiplicative digital root value 2.
%C A263477 First differences of A263471.
%H A263477 Hiroaki Yamanouchi, <a href="/A263477/b263477.txt">Table of n, a(n) for n = 1..50</a>
%H A263477 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativeDigitalRoot.html">Multiplicative Digital Root</a>
%F A263477 A263476(n) + A000012(n) + a(n) + A000027(n) + A263478(n) + A263479(n) + A263480(n) + A000027(n) + A263481(n) + A000217(n) = A052268(n).
%t A263477 Last /@ Tally@ IntegerLength@ Select[Range@ 1000000, FixedPoint[Times @@ IntegerDigits@ # &, #] == 2 &] (* _Michael De Vlieger_, Oct 21 2015 *)
%o A263477 (PARI) t(k) = {while(k>9, k=prod(i=1, #k=digits(k), k[i])); k}
%o A263477 a(n) = sum(i=10^(n-1), 10^n - 1, if(t(i) == 2, 1, 0)); \\ _Altug Alkan_, Oct 19 2015
%Y A263477 Cf. A031347, A034049, A051813, A263471.
%K A263477 nonn,base
%O A263477 1,2
%A A263477 _Martin Renner_, Oct 19 2015
%E A263477 a(9)-a(23) from _Hiroaki Yamanouchi_, Oct 25 2015