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
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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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
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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
Comments