A111065 Numbers that look the same when rotated by 180 degrees, using only digits 0, 6 and 9.

0, 69, 96, 609, 906, 6009, 6699, 6969, 9006, 9696, 9966, 60009, 66099, 69069, 90006, 96096, 99066, 600009, 606909, 609609, 660099, 666999, 669699, 690069, 696969, 699669, 900006, 906906, 909606, 960096, 966996, 969696, 990066, 996966, 999666, 6000009, 6060909

Offset

1,2

Comments

Strobogrammatic numbers (A000787) without digits 1 or 8.

Apparently this sequence and A006072 have the same parity. - Jeremy Gardiner, Oct 15 2005

There are no primes in this sequence because all terms are divisible by 3. - M. F. Hasler, May 04 2012

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Mathematica

fQ[n_] := Block[{s = {0, 6, 9}, id = IntegerDigits[n]}, If[ Union[ Join[s, id]] == s && (id /. {6 -> 9, 9 -> 6}) == Reverse[id], True, False]]; Select[ Range[0, 10^6], fQ[ # ] &] (Robert G. Wilson v, Oct 11 2005)

Prog

(Haskell) main=print$"0":concat[concat[[reverse(reverse(map f x)++z++x)|x<-y]|z<-["", "0"]]|y<-s(iterate i"6")]; f '0'='0'; f '6'='9'; f '9'='6'; i('0':x)='6':x; i('6':x)='9':x; i('9':x)='0':i x; i""="6"; s(x:y@(z:_))=let w:v=s y in if length x==length z then(x:w):v else[x]:w:v
(PARI) is_A111065(n)=!setminus(Set(n=Vec(Str(n))), Vec("069")) & apply(t->Vec("096")[max(eval(t)/3, 1)], n)==vecextract(n, "-1..1")  \\ M. F. Hasler, May 04 2012
(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 0
    for d in count(2):
        for start in "69":
            for rest in product("069", repeat=d//2-1):
                left = start + "".join(rest)
                right = ud(left)
                for mid in [[""], ["0"]][d%2]:
                    yield int(left + mid + right)
print(list(islice(agen(), 37))) # Michael S. Branicky, Mar 29 2022

Crossrefs

Cf. strobogrammatic numbers A000787. If 8's are included we get A111156.

Sequence in context: A043257 A044037 A287092 * A227271 A004237 A004238

Adjacent sequences: A111062 A111063 A111064 * A111066 A111067 A111068

Keyword

base,easy,nonn

Author

Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 08 2005

Extensions

Offset corrected by Reinhard Zumkeller, Sep 26 2014

a(36) and beyond from Michael S. Branicky, Mar 29 2022

Status

approved