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A000787
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Strobogrammatic numbers: the same upside down.
(Formerly M4480 N1897)
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24
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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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.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A007597 (Primes in this sequence), A057770, A111065, A169731 (another version).
Subsequence of A045574. - M. F. Hasler, May 04 2012
Sequence in context: A107788 A038289 A079607 * A188000 A167621 A289287
Adjacent sequences: A000784 A000785 A000786 * A000788 A000789 A000790
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KEYWORD
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base,nonn,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from Robert G. Wilson v, Oct 11 2005
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STATUS
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approved
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