A169731 Numbers that are the same upside down (using only digits 0, 1, 6 and 9).

0, 1, 11, 69, 96, 101, 111, 609, 619, 906, 916, 1001, 1111, 1691, 1961, 6009, 6119, 6699, 6969, 9006, 9116, 9696, 9966, 10001, 10101, 11011, 11111, 16091, 16191, 19061, 19161, 60009, 60109, 61019, 61119, 66099, 66199, 69069, 69169, 90006, 90106, 91016, 91116

Offset: 1

Author

N. J. A. Sloane, May 01 2010, based on a suggestion from Terry Stickels

Keywords

• nonn
• base
• easy

Comments

A000787 without using digit 8, considered here as composed of two circles with different radius. 'Same upside down' means central symmetric, that is 180-degree rotationally symmetric about a central axis perpendicular to the screen plane. See the comment by M. F. Hasler in A000787. - Wolfdieter Lang, Oct 25 2013

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1535 from T. D. Noe)

Crossrefs

Cf. A000787.

Programs

Python

from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def agen():
    yield from [0, 1]
    for d in count(2):
        for start in "169":
            for rest in product("0169", repeat=d//2-1):
                left = start + "".join(rest)
                right = ud(left)
                for mid in [[""], ["0", "1"]][d%2]:
                    yield int(left + mid + right)
print(list(islice(agen(), 43))) # Michael S. Branicky, Mar 29 2022

Extensions

Extended by T. D. Noe, May 03 2010