A018846 Strobogrammatic numbers: numbers that are the same upside down (using calculator-style numerals).

0, 1, 2, 5, 8, 11, 22, 55, 69, 88, 96, 101, 111, 121, 151, 181, 202, 212, 222, 252, 282, 505, 515, 525, 555, 585, 609, 619, 629, 659, 689, 808, 818, 828, 858, 888, 906, 916, 926, 956, 986, 1001, 1111, 1221, 1551, 1691, 1881, 1961, 2002, 2112, 2222, 2552, 2692, 2882

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base
• easy
• nice

Comments

A018847 lists primes in this sequence. - M. F. Hasler, May 05 2012

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A053701 (vertically symmetric numbers), A048708.

Programs

PARI

is_A018846(n,t=Vec("012..59.86"))={ apply(x->t[eval(x)+1], n=Vec(Str(n)))==vecextract(n, "-1..1") } \\ M. F. Hasler, May 05 2012

Python

from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def A018846gen(): # generator of terms
    yield from [0, 1, 2, 5, 8]
    for d in count(2):
        for first in "125689":
            for rest in product("0125689", repeat=d//2-1):
                left = first + "".join(rest)
                for mid in [[""], ["0", "1", "2", "5", "8"]][d%2]:
                    yield int(left + mid + ud(left))
print(list(islice(A018846gen(), 54))) # Michael S. Branicky, Jul 09 2022