A090077 In binary expansion of n: reduce contiguous blocks of 1's to 1.

0, 1, 2, 1, 4, 5, 2, 1, 8, 9, 10, 5, 4, 5, 2, 1, 16, 17, 18, 9, 20, 21, 10, 5, 8, 9, 10, 5, 4, 5, 2, 1, 32, 33, 34, 17, 36, 37, 18, 9, 40, 41, 42, 21, 20, 21, 10, 5, 16, 17, 18, 9, 20, 21, 10, 5, 8, 9, 10, 5, 4, 5, 2, 1, 64, 65, 66, 33, 68, 69, 34, 17, 72, 73, 74, 37, 36, 37, 18, 9

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2003

Keywords

• nonn
• base

Examples

			100 -> '1100100' -> [11]00[1]00 -> [1]00[1]00 -> '100100' -> 36=a(100).
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007088, A090079, A090078, A348710.

Programs

Mathematica

Array[FromDigits[Flatten[Split@ IntegerDigits[#, 2] /. w_List /; First[w] == 1 -> {1}], 2] &, 80, 0] (* Michael De Vlieger, Jul 28 2022 *)

Python

def a(n):
    b = bin(n)[2:]
    while "11" in b: b = b.replace("11", "1")
    return int(b, 2)
print([a(n) for n in range(81)]) # Michael S. Branicky, Jul 27 2022

Formula

a(a(n)) = a(n); a(A090078(n)) = A090078(a(n)) = A090079(n).

a(A003714(n)) = A003714(n); a(A004780(n)) < A004780(n); a(n) <= A179821(n); A085357(a(n)) = 1. - Reinhard Zumkeller, Jul 31 2010