A169731 -id:A169731 - cp's OEIS frontend

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

N. J. A. Sloane

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

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).

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.

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

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

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 *)

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

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

A246880 6((10^n-1)/9)(10^(n+1))+9*(10^n-1)/9.

Original entry on oeis.org

0, 609, 66099, 6660999, 666609999, 66666099999, 6666660999999, 666666609999999, 66666666099999999, 6666666660999999999, 666666666609999999999, 66666666666099999999999, 6666666666660999999999999, 666666666666609999999999999, 66666666666666099999999999999

Offset: 0

Felix Fröhlich, Sep 06 2014

Numbers of the form 6...609...9 (i.e., consisting of an odd number of digits with the middle digit 0, all digits to the left of the middle digit 6 and all digits to the right of the middle digit 9).

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Subsequence of A001743, A039434, A111065, A111156, A153806, A169731 and A227793.

[(6*((10^n - 1)/9))*(10^(n + 1)) + (9*(10^n - 1)/9) : n in [0..15]]; // Wesley Ivan Hurt, Sep 15 2014

A246880:=n->(6*((10^n - 1)/9))*(10^(n + 1)) + (9*(10^n - 1)/9): seq(A246880(n),n=0..15); # Wesley Ivan Hurt, Sep 15 2014

Table[(6*((10^n - 1)/9))*(10^(n + 1)) + (9*(10^n - 1)/9), {n, 15}] (* Wesley Ivan Hurt, Sep 15 2014 *)
Join[{0}, CoefficientList[Series[20/(3 x - 300 x^2) + 1/(x^2 - x) + 17/(30 x^2 - 3 x), {x, 0, 30}], x]] (* Wesley Ivan Hurt, Sep 15 2014 *)

a(n)=6*((10^n-1)/9)*(10^(n+1))+9*(10^n-1)/9

G.f.: 20/(3-300*x)+1/(x-1)+17/(30*x-3); a(n) = 111*a(n-1)-1110*a(n-2)+1000*a(n-3). - Wesley Ivan Hurt, Sep 15 2014

A287092 Strobogrammatic nonpalindromic numbers.

Original entry on oeis.org

69, 96, 609, 619, 689, 906, 916, 986, 1691, 1961, 6009, 6119, 6699, 6889, 6969, 8698, 8968, 9006, 9116, 9696, 9886, 9966, 16091, 16191, 16891, 19061, 19161, 19861, 60009, 60109, 60809, 61019, 61119, 61819, 66099, 66199, 66899, 68089, 68189, 68889, 69069, 69169, 69869, 86098, 86198, 86898, 89068, 89168

Offset: 1

Ilya Gutkovskiy, May 19 2017

Nonpalindromic numbers which are invariant under a 180-degree rotation.
Numbers that are the same upside down and containing digits 6, 9.
Intersection of A000787 and A029742.
Union of this sequence and A006072 gives A000787.

Cf. A000787, A007597, A018848, A029742, A006072, A153806, A169731.

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, 89168], fQ[ # ] && ! PalindromeQ[ # ] &]

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A000787 Strobogrammatic numbers: the same upside down.

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A287092 Strobogrammatic nonpalindromic numbers.

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cp's OEIS Frontend

A000787 Strobogrammatic numbers: the same upside down.

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A246880 6*((10^n-1)/9)*(10^(n+1))+9*(10^n-1)/9.

Views

Author

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Magma

Maple

Mathematica

PARI

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A287092 Strobogrammatic nonpalindromic numbers.

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Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A246880 6((10^n-1)/9)(10^(n+1))+9*(10^n-1)/9.