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A034051 Numbers with multiplicative digital root value 4.

%I A034051 #41 Feb 16 2025 08:32:36
%S A034051 4,14,22,27,39,41,72,89,93,98,114,122,127,139,141,172,189,193,198,212,
%T A034051 217,221,249,266,271,277,294,319,333,338,346,364,379,383,391,397,411,
%U A034051 429,436,463,492,626,634,643,662,677,712,721,727,739,767,772,776,793
%N A034051 Numbers with multiplicative digital root value 4.
%H A034051 Robert Israel, <a href="/A034051/b034051.txt">Table of n, a(n) for n = 1..5000</a>
%H A034051 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiplicativeDigitalRoot.html">Multiplicative Digital Root</a>
%H A034051 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%p A034051 mdr:= proc(n) option remember;
%p A034051 if n < 10 then return(n) fi;
%p A034051 procname(convert(convert(n,base,10),`*`))
%p A034051 end proc:
%p A034051 select(mdr=4, [$1..10^5]); # _Robert Israel_, Oct 19 2015
%t A034051 Select[Range@ 800, FixedPoint[Times @@ IntegerDigits@ # &, #] == 4 &] (* _Michael De Vlieger_, Oct 19 2015 *)
%o A034051 (PARI) t(n) = {while(n>9, n=prod(i=1, #n=digits(n), n[i])); n};
%o A034051 for(n=0, 1e4, if(t(n) == 4, print1(n", "))); \\ _Altug Alkan_, Oct 19 2015
%Y A034051 Cf. A031347.
%Y A034051 Cf. A034048, A002275, A034049, A034050, A034051, A034052, A034053, A034054, A034055, A034056 (numbers having multiplicative digital roots 0-9).
%K A034051 nonn,base,easy
%O A034051 1,1
%A A034051 _Patrick De Geest_, Sep 15 1998
%E A034051 Incorrect formula removed by _Martin Renner_, Oct 19 2015