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

0,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to binary expansion of n

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007088, A090079, A090078, A348710.

Sequence in context: A343430 A292895 A371015 * A229763 A163509 A161399

Adjacent sequences: A090074 A090075 A090076 * A090078 A090079 A090080

Keyword

nonn,base

Author

Reinhard Zumkeller, Nov 20 2003

Status

approved