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

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

Author

Robin Powell, Jan 27 2016

Keywords

• nonn
• base

Comments

Intersection of A023705 and A032924.

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A023705, A032924, A262958, A262963.

Programs

PARI

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

Python

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