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A032822 Numbers whose set of base-10 digits is {1,4}.

%I A032822 #30 Jun 28 2025 18:10:29
%S A032822 1,4,11,14,41,44,111,114,141,144,411,414,441,444,1111,1114,1141,1144,
%T A032822 1411,1414,1441,1444,4111,4114,4141,4144,4411,4414,4441,4444,11111,
%U A032822 11114,11141,11144,11411,11414,11441,11444,14111,14114
%N A032822 Numbers whose set of base-10 digits is {1,4}.
%H A032822 Vincenzo Librandi, <a href="/A032822/b032822.txt">Table of n, a(n) for n = 1..1000</a>
%H A032822 <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.
%F A032822 a(1)=1, a(2)=4; a(n) = 10*a(floor(n/2))+1 for n odd, otherwise a(n) = 10*a(floor((n-1)/2))+4. - _Bruno Berselli_, May 28 2012
%t A032822 Flatten[Table[FromDigits[#,10]&/@Tuples[{1,4},n],{n,5}]] (* _Vincenzo Librandi_, May 28 2012 *)
%o A032822 (Magma) [n: n in [1..15000] | Set(IntegerToSequence(n, 10)) subset {1, 4}]; // _Vincenzo Librandi_, May 28 2012
%o A032822 (Maxima) a[1]:1$ a[2]:4$ a[n]:= if oddp(n) then 10*a[floor(n/2)]+1 else 10*a[floor((n-1)/2)]+4$ makelist(a[n],n,1,40); /* _Bruno Berselli_, May 28 2012 */
%o A032822 (Python)
%o A032822 def a(n): return int(bin(n+1)[3:].replace('1', '4').replace('0', '1'))
%o A032822 print([a(n) for n in range(1, 45)]) # _Michael S. Branicky_, May 13 2021
%o A032822 (Python)
%o A032822 def A032822(n): return 3*int(bin(n+1)[3:])+(10**((n+1).bit_length()-1)-1)//9 # _Chai Wah Wu_, Jun 28 2025
%Y A032822 Cf. A020452 (primes).
%K A032822 nonn,base,easy
%O A032822 1,2
%A A032822 _Clark Kimberling_