A262963 List of numbers n whose base-3 expansion contains only the digits 1 and 2 and whose base-4 expansion contains only the digits 2 and 3.

2, 14, 43, 238, 239, 698, 4010, 4090, 4091, 4094, 10922, 12031, 12271, 12283, 174842, 174847, 176062, 176063, 977578, 977579, 981679, 981691, 981931, 981934, 981935, 981950, 1043114, 1043194, 1043195, 1043198, 3129259, 3129262, 3129263, 3129322, 3129323, 3129326, 3129343

Offset: 1

Author

Robin Powell, Oct 05 2015

Keywords

• nonn
• base

Examples

			43 is 1121 in base 3 and 223 in base 4; it uses the two largest digits in the two bases and is therefore a term.
Similarly 238 is 22211 in base 3 and 3232 in base 4 so it is also a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A258981, A261970, A262958.

Programs

Python

from gmpy2 import digits
def f1(n):
    s = digits(n,3)
    m = len(s)
    for i in range(m):
        if s[i] == '0':
            return(int(s[:i]+'1'*(m-i),3))
    return n
def f2(n):
    s = digits(n,4)
    m = len(s)
    for i in range(m):
        if s[i] in ['0','1']:
            return(int(s[:i]+'2'*(m-i),4))
    return n
A262963_list = []
n = 1
for i in range(10**4):
    m = f2(f1(n))
    while m != n:
        n, m = m, f2(f1(m))
    A262963_list.append(m)
    n += 1 # Chai Wah Wu, Oct 30 2015