A261970 -id:A261970 - cp's OEIS frontend

A262958 Numbers whose base-b expansions, for both b=3 and b=4, include no digits other than 1 and b-1.

1, 5, 7, 13, 23, 53, 125, 215, 373, 1367, 1373, 1375, 3551, 4093, 5471, 5495, 5503, 30581, 30589, 32765, 32767, 56821, 56831, 89557, 96119, 96215, 96223, 97655, 98135, 98141, 98143, 98167, 98293, 98303, 351743, 352093, 521599, 521693, 521717, 521719, 524119, 524149, 875893, 875903, 884725, 884735

Offset: 1

Robin Powell, Oct 05 2015

1, 7 and 32767 also share this property in base 2; their binary expansions consist only of a sequence of 1s.

			53 is 1222 in base 3 and 311 in base 4; it only uses the digit 1 or the largest digit in the two bases and is therefore a term.
Similarly 215 is 21222 in base 3 and 3113 in base 4 so it is also a term.

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

Cf. A207079, A258981, A261970.

Select[Range@ 1000000, Last@ DigitCount[#, 3] == 0 && Total@ Rest@ Drop[DigitCount[#, 4], {3}] == 0 &] (* Michael De Vlieger, Oct 05 2015 *)
Join[{1,5},Flatten[Table[Select[FromDigits[#,3]&/@Tuples[{1,2},n], Union[ IntegerDigits[ #,4]] =={1,3}&],{n,20}]]] (* Harvey P. Dale, Jun 14 2016 *)

is(n)=!setsearch(Set(digits(n,3)),0) && #setintersect(Set(digits(n,4)),[0,2])==0 \\ Charles R Greathouse IV, Oct 12 2015

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] == '0':
            return(int(s[:i]+'1'*(m-i),4))
        if s[i] == '2':
            return(int(s[:i]+'3'+'1'*(m-i-1),4))
    return n
A262958_list = []
n = 1
for i in range(10**4):
    m = f2(f1(n))
    while m != n:
        n, m = m, f2(f1(m))
    A262958_list.append(m)
    n += 1 # Chai Wah Wu, Oct 30 2015

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.

Original entry on oeis.org

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

Robin Powell, Oct 05 2015

			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.

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

Cf. A258981, A261970, A262958.

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

cp's OEIS Frontend

A262958 Numbers whose base-b expansions, for both b=3 and b=4, include no digits other than 1 and b-1.

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