cp's OEIS Frontend

A342348 Smallest number > 3 whose representation in all bases from 2 up to n consists only of '0's, '1's, '2's and '3's.

%I A342348 #16 Mar 14 2021 21:23:14
%S A342348 4,4,4,5,6,7,8,8281
%N A342348 Smallest number > 3 whose representation in all bases from 2 up to n consists only of '0's, '1's, '2's and '3's.
%C A342348 Conjecture: there are no more terms.
%C A342348 If it exists, a(10) > 10^2000. - _Bert Dobbelaere_, Mar 14 2021
%e A342348 a(9) = 8281.
%e A342348 8281 in base 2 =  10000001011001
%e A342348 8281 in base 3 =  102100201
%e A342348 8281 in base 4 =  2001121
%e A342348 8281 in base 5 =  231111
%e A342348 8281 in base 6 =  102201
%e A342348 8281 in base 7 =  33100
%e A342348 8281 in base 8 =  20131
%e A342348 8281 in base 9 =  12321
%o A342348 (Python)
%o A342348 def only0123(n, b):
%o A342348   while n >= b:
%o A342348     n, r = divmod(n, b)
%o A342348     if r > 3: return False
%o A342348   return n <= 3
%o A342348 def a(n):
%o A342348   k = max(4, n)
%o A342348   while not all(only0123(k, b) for b in range(2, n+1)): k += 1
%o A342348   return k
%o A342348 print([a(n) for n in range(2, 10)]) # _Michael S. Branicky_, Mar 12 2021
%Y A342348 Cf. A258107.
%K A342348 nonn,base,more
%O A342348 2,1
%A A342348 _Chai Wah Wu_, Mar 12 2021