A000787 Strobogrammatic numbers: the same upside down.

0, 1, 8, 11, 69, 88, 96, 101, 111, 181, 609, 619, 689, 808, 818, 888, 906, 916, 986, 1001, 1111, 1691, 1881, 1961, 6009, 6119, 6699, 6889, 6969, 8008, 8118, 8698, 8888, 8968, 9006, 9116, 9696, 9886, 9966, 10001, 10101, 10801, 11011, 11111, 11811, 16091, 16191

Offset: 1

Author

N. J. A. Sloane

Keywords

• base
• nonn
• easy

Comments

Strobogrammatic numbers are a kind of ambigrams that retain the same meaning when viewed upside down. - Daniel Mondot, Sep 27 2016

"Upside down" here means rotated by 180 degrees (i.e., central symmetry), NOT "vertically flipped" (symmetry w.r.t. horizontal line, which are in A045574). - M. F. Hasler, May 04 2012

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
• J. M. Howell, Strobogrammatic years, Math. Mag., 34 (1961), p. 182 and 184.
• N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 5.

Crossrefs

Cf. A007597 (Primes in this sequence), A057770, A111065, A169731 (another version).

Subsequence of A045574. - M. F. Hasler, May 04 2012

Programs

Mathematica

fQ[n_] := Block[{s = {0, 1, 6, 8, 9}, id = IntegerDigits[n]}, If[ Union[ Join[s, id]] == s && (id /. {6 -> 9, 9 -> 6}) == Reverse[id], True, False]]; Select[ Range[0, 16190], fQ[ # ] &] (* Robert G. Wilson v, Oct 11 2005 *)

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, 8]
    for d in count(2):
        for start in "1689":
            for rest in product("01689", repeat=d//2-1):
                left = start + "".join(rest)
                right = ud(left)
                for mid in [[""], ["0", "1", "8"]][d%2]:
                    yield int(left + mid + right)
print(list(islice(agen(), 47))) # Michael S. Branicky, Mar 29 2022

Extensions

More terms from Robert G. Wilson v, Oct 11 2005