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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.
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
1,1
EXAMPLE
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.
PROG
(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
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Robin Powell, Oct 05 2015
STATUS
approved