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%I #36 Jan 24 2023 02:56:57
%S 2,12,21,26,34,37,43,62,73,112,121,126,134,137,143,162,173,211,216,
%T 223,232,261,278,279,287,297,299,314,317,322,341,367,369,371,376,389,
%U 396,398,413,431,447,469,474,496,612,621,637,639,649,666,673,693,694,713
%N Numbers with multiplicative digital root value 2.
%H Robert Israel, <a href="/A034049/b034049.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiplicativeDigitalRoot.html">Multiplicative Digital Root</a>
%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%p A031347:= proc(n) local x;
%p x:= n;
%p while x > 10 do
%p x:= convert(convert(x,base,10),`*`)
%p od;
%p x
%p end proc:
%p select(A031347=2, [$1..1000]); # _Robert Israel_, Jan 23 2023
%t 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 (PARI) t(n) = {while(n>9, n=prod(i=1, #n=digits(n), n[i])); n};
%o for(n=0, 1e3, if(t(n) == 2, print1(n", "))); \\ _Altug Alkan_, Oct 19 2015
%Y Cf. A031347.
%Y Cf. A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).
%K nonn,base
%O 1,1
%A _Patrick De Geest_, Sep 15 1998
%E Incorrect formula removed by _Martin Renner_, Oct 19 2015
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