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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.
0
4, 4, 4, 5, 6, 7, 8, 8281
OFFSET
2,1
COMMENTS
Conjecture: there are no more terms.
If it exists, a(10) > 10^2000. - Bert Dobbelaere, Mar 14 2021
EXAMPLE
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
PROG
(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
CROSSREFS
Cf. A258107.
Sequence in context: A036854 A036858 A131957 * A127932 A006075 A342576
KEYWORD
nonn,base,more
AUTHOR
Chai Wah Wu, Mar 12 2021
STATUS
approved