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Numbers k such that the product of the digits of k is not the product of digits of any earlier term in the sequence.
2

%I #30 Jun 13 2021 03:24:33

%S 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 58,59,67,68,69,77,78,79,88,89,99,255,256,257,258,259,267,268,269,277,

%U 278,279,288,289,299,355,357,358,359,377,378,379,388,389,399,455

%N 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 Observations:

%C The digits 0 and 1 appear only in terms 0 and 1, respectively.

%C 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 Digits in each term appear in ascending order (A009994).

%H Rémy Sigrist, <a href="/A343403/b343403.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A343403/a343403.gp.txt">PARI program for A343403</a>

%p # product of digits

%p A007954 := proc(n::integer)

%p if n = 0 then

%p 0;

%p else

%p mul( d, d=convert(n, base, 10)) ;

%p end if;

%p end proc:

%p hit:=Array(0..10000,-1);

%p a:=[0];

%p hit[0]:=0;

%p for n from 1 to 50000 do p:=A007954(n);

%p if p>0 and hit[p]=-1 then hit[p]:=n; a:=[op(a),n]; fi; od:

%p a; # _N. J. A. Sloane_, Apr 14 2021

%o (Python 3.7)

%o def getBaseTen(howMany=100):

%o listToReturn = []

%o listOfObtainedValues = []

%o count = 0

%o while len(listToReturn) < howMany:

%o afterOnePermutation = 1

%o for num in str(count):

%o afterOnePermutation *= int(num)

%o if afterOnePermutation is 0:

%o break

%o if not afterOnePermutation in listOfObtainedValues:

%o listToReturn.append(str(count))

%o listOfObtainedValues.append(afterOnePermutation)

%o count += 1

%o return listToReturn

%o (PARI) See Links section.

%Y Cf. A003001, A007954, A009994 (ascending digits), A031346, A068189, A343160.

%K nonn,base

%O 1,3

%A _Collin King_, Apr 14 2021