A262958 -id:A262958 - cp's OEIS frontend

A261970 Numbers whose base-b expansions, for both b=3 and b=4, include no digits other than 0 and b-1.

0, 60, 240, 13308, 52992, 53052, 53196, 3195132, 3208140, 3346188, 12795648, 12795900, 871563264, 871563312, 871563456, 871576368, 871576380, 871576524, 871615728, 871616268, 871616448, 1072939776, 1072939788, 1072939824, 3225157884, 3472949196, 3473670912

Offset: 1

Robin Powell, Sep 21 2015

			60 is 2020 in base 3 and 330 in base 4; it uses the largest digits in the two bases (including 0's) and is therefore a term.
Similarly 240 is 22220 in base 3 and 3300 in base 4 so it is also a term.

Paul Tek, Table of n, a(n) for n = 1..10000
Paul Tek, PARI program for this sequence

Cf. A258981, A262958.

isokb(n, b) = {if (!n, return (1)); my(d = digits(n, b)); (#vecsort(d,,8)==2) && (vecmin(d) == 0) && (vecmax(d) == b - 1);}
isok(n) = isokb(n, 3) && isokb(n, 4); \\ Michel Marcus, Sep 22 2015

More terms from Alois P. Heinz, Sep 21 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

A266001 Numbers with no 0's in their base 3 and base 4 expansions.

Original entry on oeis.org

1, 2, 5, 7, 13, 14, 22, 23, 25, 26, 41, 43, 53, 121, 122, 125, 149, 151, 157, 158, 214, 215, 229, 230, 233, 238, 239, 365, 367, 373, 374, 377, 445, 446, 473, 475, 485, 607, 617, 619, 634, 635, 637, 638, 697, 698, 701, 725, 727, 1366, 1367, 1373, 1375, 1429, 1430, 1445, 1447, 1453, 1454

Offset: 1

Robin Powell, Jan 27 2016

Intersection of A023705 and A032924.

1, 7 and 32767 also share this property in base 2.

			53 is 1222 in base 3 and 311 in base 4; no zeros are shown in either representation and so 53 is a term.
Similarly, 121 is 11111 in base 3 and 1321 in base 4 so it is also a term.

Chai Wah Wu, Table of n, a(n) for n = 1..12682

Cf. A023705, A032924, A262958, A262963.

isokd(n) = vecmin(digits(n, 3)) && vecmin(digits(n, 4)); \\ Michel Marcus, Jan 28 2016

from _future_ import division
from gmpy2 import digits
A266001_list = [j for j in (int(format(i,'b'),3)+(3**n-1)//2 for n in range(1,10) for i in range(2**n)) if '0' not in digits(j,4)] # Chai Wah Wu, Feb 13 2016

cp's OEIS Frontend

A261970 Numbers whose base-b expansions, for both b=3 and b=4, include no digits other than 0 and b-1.

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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.

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Python

A266001 Numbers with no 0's in their base 3 and base 4 expansions.

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Author

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Examples

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Programs

PARI

Python