A342348 - OEIS

%I #16 Mar 14 2021 21:23:14

%S 4,4,4,5,6,7,8,8281

%N 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 Conjecture: there are no more terms.

%C If it exists, a(10) > 10^2000. - _Bert Dobbelaere_, Mar 14 2021

%e a(9) = 8281.

%e 8281 in base 2 =  10000001011001

%e 8281 in base 3 =  102100201

%e 8281 in base 4 =  2001121

%e 8281 in base 5 =  231111

%e 8281 in base 6 =  102201

%e 8281 in base 7 =  33100

%e 8281 in base 8 =  20131

%e 8281 in base 9 =  12321

%o (Python)

%o def only0123(n, b):

%o   while n >= b:

%o     n, r = divmod(n, b)

%o     if r > 3: return False

%o   return n <= 3

%o def a(n):

%o   k = max(4, n)

%o   while not all(only0123(k, b) for b in range(2, n+1)): k += 1

%o   return k

%o print([a(n) for n in range(2, 10)]) # _Michael S. Branicky_, Mar 12 2021

%Y Cf. A258107.

%K nonn,base,more

%O 2,1

%A _Chai Wah Wu_, Mar 12 2021