A111156 Numbers that look the same when printed upside down.

0, 8, 69, 88, 96, 609, 689, 808, 888, 906, 986, 6009, 6699, 6889, 6969, 8008, 8698, 8888, 8968, 9006, 9696, 9886, 9966, 60009, 60809, 66099, 66899, 68089, 68889, 69069, 69869, 80008, 80808, 86098, 86898, 88088, 88888, 89068, 89868, 90006, 90806, 96096, 96896, 98086, 98886, 99066, 99866, 600009

Offset

1,2

Comments

Numbers with 1's are excluded.

Numbers written with digits 0,6,8,9, with 6 and 9 interchanged when reversed. - Robert Israel, Jul 02 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(n) local L, Lp, nl;
   L:= subs(1=6, 2=8, 3=9, convert(n, base, 4));
   nl:= nops(L);
   Lp:= subs([6=9, 9=6], L);
   add(Lp[-i]*10^(i-1), i=1..nl)+add(L[i]*10^(nl+i-1), i=1..nl);
end proc:
g:= proc(n) local L, Lp, nl;
   L:= subs(1=6, 2=8, 3=9, convert(n, base, 4));
   nl:= nops(L);
   Lp:= subs([6=9, 9=6], L);
   seq(add(Lp[-i]*10^(i-1), i=1..nl)+x*10^nl+add(L[i]*10^(nl+i), i=1..nl), x=[0, 8]);
end proc:
0, 8, seq(op([seq(f(n), n=4^i..4^(i+1)-1), seq(g(n), n=4^i..4^(i+1)-1)]), i=0..2); # Robert Israel, Jul 02 2018

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 '8'='8'; f '9'='6'; i('0':x)='6':x; i('6':x)='8':x; i('8':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
(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, 8]
    for d in count(2):
        for start in "689":
            for rest in product("0689", repeat=d//2-1):
                left = start + "".join(rest)
                right = ud(left)
                for mid in [[""], ["0", "8"]][d%2]:
                    yield int(left + mid + right)
print(list(islice(agen(), 48))) # Michael S. Branicky, Mar 29 2022

Crossrefs

Cf. strobogrammatic numbers A000787. If 8's are excluded we get A111065.

Sequence in context: A303010 A087487 A178368 * A297633 A152279 A015575

Adjacent sequences: A111153 A111154 A111155 * A111157 A111158 A111159

Keyword

base,easy,nonn

Author

Paul Stoeber (pstoeber(AT)uni-potsdam.de), Oct 09 2005

Extensions

Corrected by Robert Israel, Jul 02 2018

Status

approved