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A255805 Numbers with no zeros in base-8 representation.

%I A255805 #20 Jun 28 2025 15:48:27
%S A255805 1,2,3,4,5,6,7,9,10,11,12,13,14,15,17,18,19,20,21,22,23,25,26,27,28,
%T A255805 29,30,31,33,34,35,36,37,38,39,41,42,43,44,45,46,47,49,50,51,52,53,54,
%U A255805 55,57,58,59,60,61,62,63,73,74,75,76,77,78,79,81,82,83,84
%N A255805 Numbers with no zeros in base-8 representation.
%C A255805 Different from A047592, A207481.
%H A255805 Reinhard Zumkeller, <a href="/A255805/b255805.txt">Table of n, a(n) for n = 1..10000</a>
%H A255805 Wikipedia, <a href="http://www.wikipedia.org/wiki/Octal">Octal</a>
%H A255805 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%t A255805 Select[Range[100],DigitCount[#,8,0]==0&] (* _Harvey P. Dale_, Jun 08 2015 *)
%o A255805 (Haskell)
%o A255805 a255805 n = a255805_list !! (n-1)
%o A255805 a255805_list = iterate f 1 where
%o A255805    f x = 1 + if r < 7 then x else 8 * f x'  where (x', r) = divMod x 8
%o A255805 (PARI) isok(m) = vecmin(digits(m,8)) > 0; \\ _Michel Marcus_, Jan 23 2022
%o A255805 (Python)
%o A255805 def ok(n): return '0' not in oct(n)[2:]
%o A255805 print([k for k in range(85) if ok(k)]) # _Michael S. Branicky_, Jan 23 2022
%o A255805 (Python)
%o A255805 from sympy import integer_log
%o A255805 def A255805(n):
%o A255805     m = integer_log(k:=6*n+1,7)[0]
%o A255805     return sum(1+(k-7**m)//(6*7**j)%7<<3*j for j in range(m)) # _Chai Wah Wu_, Jun 28 2025
%Y A255805 Cf. A007094, A100970 (subsequence).
%Y A255805 Zeroless numbers in some other bases <= 10:  A000042 (base 2), A032924 (base 3), A023705 (base 4), A248910 (base 6), A255808 (base 9), A052382 (base 10).
%K A255805 nonn,base,easy
%O A255805 1,2
%A A255805 _Reinhard Zumkeller_, Mar 08 2015