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%I #25 Feb 13 2017 20:36:12
%S 7,17,71,117,171,711,1117,1171,1711,7111,11117,11171,11711,17111,
%T 71111,111117,111171,111711,117111,171111,711111,1111117,1111171,
%U 1111711,1117111,1171111,1711111,7111111,11111117,11111171,11111711,11117111
%N Numbers with multiplicative digital root value 7.
%C Numbers with one 7, and zero or more 1s. - _Daniel Forgues_, Oct 09 2011
%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>.
%F There are n(n+1)/2 elements up to 10^n, so a(n) is about 10^sqrt(2n).
%t Sort[Flatten[Table[FromDigits/@Permutations[Join[{7},PadRight[{},n,1]]],{n,0,10}]]] (* _Harvey P. Dale_, Jul 20 2015 *)
%o (PARI) t(k)=while(k>9, k=prod(i=1, #k=digits(k), k[i])); k
%o for(n=1, 1e8, if(t(n) == 7, print1(n, ", "))); \\ _Altug Alkan_, Oct 22 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,easy
%O 1,1
%A _Patrick De Geest_, Sep 15 1998
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