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

%I A111065 #27 Aug 12 2025 02:27:08
%S A111065 0,69,96,609,906,6009,6699,6969,9006,9696,9966,60009,66099,69069,
%T A111065 90006,96096,99066,600009,606909,609609,660099,666999,669699,690069,
%U A111065 696969,699669,900006,906906,909606,960096,966996,969696,990066,996966,999666,6000009,6060909
%N A111065 Numbers that look the same when rotated by 180 degrees, using only digits 0, 6 and 9.
%C A111065 Strobogrammatic numbers (A000787) without digits 1 or 8.
%C A111065 Apparently this sequence and A006072 have the same parity. - _Jeremy Gardiner_, Oct 15 2005
%C A111065 There are no primes in this sequence because all terms are divisible by 3. - _M. F. Hasler_, May 04 2012
%H A111065 Michael S. Branicky, <a href="/A111065/b111065.txt">Table of n, a(n) for n = 1..10000</a>
%t A111065 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 *)
%o A111065 (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
%o A111065 (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
%o A111065 (Python)
%o A111065 from itertools import count, islice, product
%o A111065 def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
%o A111065 def agen():
%o A111065     yield 0
%o A111065     for d in count(2):
%o A111065         for start in "69":
%o A111065             for rest in product("069", repeat=d//2-1):
%o A111065                 left = start + "".join(rest)
%o A111065                 right = ud(left)
%o A111065                 for mid in [[""], ["0"]][d%2]:
%o A111065                     yield int(left + mid + right)
%o A111065 print(list(islice(agen(), 37))) # _Michael S. Branicky_, Mar 29 2022
%Y A111065 Cf. strobogrammatic numbers A000787. If 8's are included we get A111156.
%K A111065 base,easy,nonn
%O A111065 1,2
%A A111065 Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 08 2005
%E A111065 Offset corrected by _Reinhard Zumkeller_, Sep 26 2014
%E A111065 a(36) and beyond from _Michael S. Branicky_, Mar 29 2022