A090078 In binary expansion of n, reduce contiguous blocks of 0's to 0.

0, 1, 2, 3, 2, 5, 6, 7, 2, 5, 10, 11, 6, 13, 14, 15, 2, 5, 10, 11, 10, 21, 22, 23, 6, 13, 26, 27, 14, 29, 30, 31, 2, 5, 10, 11, 10, 21, 22, 23, 10, 21, 42, 43, 22, 45, 46, 47, 6, 13, 26, 27, 26, 53, 54, 55, 14, 29, 58, 59, 30, 61, 62, 63, 2, 5, 10, 11, 10, 21, 22, 23, 10, 21

Offset: 0

Author

Reinhard Zumkeller, Nov 20 2003

Keywords

• nonn
• base
• easy

Examples

			100 -> '1100100' -> 11[00]1[00] -> 11[0]1[0] -> '11010' -> 26=a(100).
		

Links

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

Crossrefs

Cf. A090077, A090079, A007088.

Programs

Mathematica

a[n_] := FromDigits[Flatten[Split[IntegerDigits[n, 2]] /. x_List /; x[[1]] == 0 -> {0}], 2]; Array[a, 100, 0] (* Amiram Eldar, Jul 30 2025 *)

PARI

a(n)=my(v=binary(n),t); for(i=1,#v, if(v[i], t+=t+1, t%2, t+=t)); t \\ Charles R Greathouse IV, Aug 17 2016

Python

def a(n):
    b = bin(n)[2:]
    while "00" in b: b = b.replace("00", "0")
    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(A090077(n)) = A090077(a(n)) = A090079(n).