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A096681 Least k such that decimal representation of k*n contains only digits 0 and 2.

%I A096681 #18 Feb 01 2021 16:46:11
%S A096681 2,1,74,5,4,37,286,25,24691358,2,2,185,154,143,148,125,1306,12345679,
%T A096681 1158,1,962,1,9574,925,8,77,81563786,715,75938,74,7162,625,6734,653,
%U A096681 572,61728395,6,579,518,5,542,481,51214,5,49382716,4787,426,4625,44898,4
%N A096681 Least k such that decimal representation of k*n contains only digits 0 and 2.
%H A096681 Robert G. Wilson v, <a href="/A096681/b096681.txt">Table of n, a(n) for n = 1..10000</a>
%F A096681 a(n) = A078241(n)/n.
%o A096681 (PARI) isok(n) = my(vd = vecsort(digits(n),,8)); (vd == [0,2]) || (vd == [2]);
%o A096681 a(n) = my(k=1); while(!isok(k*n), k++); k; \\ _Michel Marcus_, Sep 25 2016
%o A096681 (Python)
%o A096681 def next02(n):
%o A096681   s = str(n)
%o A096681   if s > '2'*len(s): return int('2' + '0'*len(s))
%o A096681   for i, c in enumerate(s):
%o A096681     if c == '1': return int(s[:i] + '2' + '0'*(len(s)-i-1))
%o A096681     elif s[i:] > '2'*(len(s)-i): return int(s[:i-1] + '2' + '0'*(len(s)-i))
%o A096681 def a(n):
%o A096681   k = 1
%o A096681   while set(str(k*n)) - set('02') != set(): k = max(k+1, next02(k*n)//n)
%o A096681   return k
%o A096681 print([a(n) for n in range(1, 51)]) # _Michael S. Branicky_, Feb 01 2021
%Y A096681 Cf. A004290, A078241-A078248, A079339, A096682, A096683, A096684, A096685, A096686, A096687, A096688.
%K A096681 base,nonn
%O A096681 1,1
%A A096681 _Ray Chandler_, Jul 12 2004