A038585 Write n in binary, delete 0's.

1, 1, 11, 1, 11, 11, 111, 1, 11, 11, 111, 11, 111, 111, 1111, 1, 11, 11, 111, 11, 111, 111, 1111, 11, 111, 111, 1111, 111, 1111, 1111, 11111, 1, 11, 11, 111, 11, 111, 111, 1111, 11, 111, 111, 1111, 111, 1111, 1111, 11111, 11, 111, 111, 1111, 111, 1111, 1111

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base
• nice

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A000120, A002275, A038573.

Programs

Haskell

a038585 0 = 0
a038585 n = (9 * m + 1) * (a038585 n') + m where (n', m) = divMod n 2
-- Reinhard Zumkeller, Oct 10 2012

Mathematica

Table[FromDigits[DeleteCases[IntegerDigits[n,2],?(#==0&)]],{n,60}] (* _Harvey P. Dale, Feb 27 2012 *)
FromDigits/@(IntegerDigits[Range[60],2]/.(0->Nothing)) (* Harvey P. Dale, Apr 09 2017 *)

Python

def A038585(n):
    return int(bin(n)[2:].replace('0','')) # Chai Wah Wu, May 19 2020

Formula

a(n) = (9 * n mod 2 + 1) * a(floor(n/2)) + n mod 2. - Reinhard Zumkeller, Oct 10 2012

a(n) = A002275(A000120(n)). - Chai Wah Wu, May 19 2020

Extensions

More terms from Erich Friedman