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A034049 Numbers with multiplicative digital root value 2.

%I A034049 #37 Feb 16 2025 08:32:36
%S A034049 2,12,21,26,34,37,43,62,73,112,121,126,134,137,143,162,173,211,216,
%T A034049 223,232,261,278,279,287,297,299,314,317,322,341,367,369,371,376,389,
%U A034049 396,398,413,431,447,469,474,496,612,621,637,639,649,666,673,693,694,713
%N A034049 Numbers with multiplicative digital root value 2.
%H A034049 Robert Israel, <a href="/A034049/b034049.txt">Table of n, a(n) for n = 1..10000</a>
%H A034049 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativeDigitalRoot.html">Multiplicative Digital Root</a>
%H A034049 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%p A034049 A031347:= proc(n) local x;
%p A034049   x:= n;
%p A034049   while x > 10 do
%p A034049     x:= convert(convert(x,base,10),`*`)
%p A034049   od;
%p A034049   x
%p A034049 end proc:
%p A034049 select(A031347=2, [$1..1000]); # _Robert Israel_, Jan 23 2023
%t A034049 t = {}; n = 0; While[Length[t] < 100, n++; s = n; While[s > 10, s = Times @@ IntegerDigits[s]]; If[s == 2, AppendTo[t, n]]]; t (* _T. D. Noe_, Nov 15 2011 *)
%o A034049 (PARI) t(n) = {while(n>9, n=prod(i=1, #n=digits(n), n[i])); n};
%o A034049 for(n=0, 1e3, if(t(n) == 2, print1(n", "))); \\ _Altug Alkan_, Oct 19 2015
%Y A034049 Cf. A031347.
%Y A034049 Cf. A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).
%K A034049 nonn,base
%O A034049 1,1
%A A034049 _Patrick De Geest_, Sep 15 1998
%E A034049 Incorrect formula removed by _Martin Renner_, Oct 19 2015