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A343403 Numbers k such that the product of the digits of k is not the product of digits of any earlier term in the sequence.

%I A343403 #30 Jun 13 2021 03:24:33
%S A343403 0,1,2,3,4,5,6,7,8,9,25,26,27,28,29,35,37,38,39,45,47,48,49,55,56,57,
%T A343403 58,59,67,68,69,77,78,79,88,89,99,255,256,257,258,259,267,268,269,277,
%U A343403 278,279,288,289,299,355,357,358,359,377,378,379,388,389,399,455
%N A343403 Numbers k such that the product of the digits of k is not the product of digits of any earlier term in the sequence.
%C A343403 Observations:
%C A343403 The digits 0 and 1 appear only in terms 0 and 1, respectively.
%C A343403 Terms cannot contain two 2s, two 3s, a 2 and a 3, a 2 and a 4, a 3 and a 4, or a 4 and a 6.
%C A343403 Digits in each term appear in ascending order (A009994).
%H A343403 Rémy Sigrist, <a href="/A343403/b343403.txt">Table of n, a(n) for n = 1..10000</a>
%H A343403 Rémy Sigrist, <a href="/A343403/a343403.gp.txt">PARI program for A343403</a>
%p A343403 # product of digits
%p A343403 A007954 := proc(n::integer)
%p A343403     if n = 0 then
%p A343403         0;
%p A343403     else
%p A343403         mul( d, d=convert(n, base, 10)) ;
%p A343403     end if;
%p A343403 end proc:
%p A343403 hit:=Array(0..10000,-1);
%p A343403 a:=[0];
%p A343403 hit[0]:=0;
%p A343403 for n from 1 to 50000 do p:=A007954(n);
%p A343403    if p>0 and hit[p]=-1 then hit[p]:=n; a:=[op(a),n]; fi; od:
%p A343403 a; # _N. J. A. Sloane_, Apr 14 2021
%o A343403 (Python 3.7)
%o A343403 def getBaseTen(howMany=100):
%o A343403     listToReturn = []
%o A343403     listOfObtainedValues = []
%o A343403     count = 0
%o A343403     while len(listToReturn) < howMany:
%o A343403         afterOnePermutation = 1
%o A343403         for num in str(count):
%o A343403             afterOnePermutation *= int(num)
%o A343403             if afterOnePermutation is 0:
%o A343403                 break
%o A343403         if not afterOnePermutation in listOfObtainedValues:
%o A343403             listToReturn.append(str(count))
%o A343403             listOfObtainedValues.append(afterOnePermutation)
%o A343403         count += 1
%o A343403     return listToReturn
%o A343403 (PARI) See Links section.
%Y A343403 Cf. A003001, A007954, A009994 (ascending digits), A031346, A068189, A343160.
%K A343403 nonn,base
%O A343403 1,3
%A A343403 _Collin King_, Apr 14 2021