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.

4, 4, 4, 5, 6, 7, 8, 8281

Offset: 2

Author

Chai Wah Wu, Mar 12 2021

Keywords

• nonn
• base
• more

Comments

Conjecture: there are no more terms.

If it exists, a(10) > 10^2000. - Bert Dobbelaere, Mar 14 2021

Examples

			a(9) = 8281.
8281 in base 2 =  10000001011001
8281 in base 3 =  102100201
8281 in base 4 =  2001121
8281 in base 5 =  231111
8281 in base 6 =  102201
8281 in base 7 =  33100
8281 in base 8 =  20131
8281 in base 9 =  12321
		

Crossrefs

Cf. A258107.

Programs

Python

def only0123(n, b):
  while n >= b:
    n, r = divmod(n, b)
    if r > 3: return False
  return n <= 3
def a(n):
  k = max(4, n)
  while not all(only0123(k, b) for b in range(2, n+1)): k += 1
  return k
print([a(n) for n in range(2, 10)]) # Michael S. Branicky, Mar 12 2021