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

Author

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

Keywords

• base
• easy
• nonn

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

Crossrefs

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

Programs

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

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 *)

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

Extensions

Offset corrected by Reinhard Zumkeller, Sep 26 2014

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