A090079 In binary expansion of n: reduce contiguous blocks of 0's to 0 and contiguous blocks of 1's to 1.

0, 1, 2, 1, 2, 5, 2, 1, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 10, 21, 42, 21, 10, 21, 10, 5, 2, 5, 10, 5, 10, 21, 10, 5, 2, 5, 10, 5, 2, 5, 2, 1, 2, 5, 10, 5, 10, 21, 10, 5, 10, 21, 42, 21, 10, 21, 10, 5, 10, 21, 42, 21

Offset

0,3

Comments

a(a(n))=a(n); a(n)=A090078(A090077(n))=A090077(A090078(n)).

All terms are without consecutive equal binary digits: a(A000975(n)) = A000975(n) and a(m) <> A000975(n) for m < A000975(n). - Reinhard Zumkeller, Feb 16 2013

Links

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

Index entries for sequences related to binary expansion of n

Formula

Conjecture: a(n) = (2^(A005811(n)+1) + (1-(-1)^n)/2 - 2)/3. - Velin Yanev, Dec 12 2016

Example

100 -> '1100100' -> [11][00][1][00] -> [1][0][1][0] -> '1010' ->
10=a(100).

Mathematica

Table[FromDigits[#, 2] &@ Map[First, Split@ IntegerDigits[n, 2]], {n, 0, 83}] (* Michael De Vlieger, Dec 12 2016 *)
FromDigits[Split[IntegerDigits[#, 2]][[All, 1]], 2]&/@Range[0, 90] (* Harvey P. Dale, Oct 10 2017 *)

Prog

(Haskell)
a090079 = foldr (\b v -> 2 * v + b) 0 . map head . group . a030308_row
-- Reinhard Zumkeller, Feb 16 2013
(Python)
from itertools import groupby
def a(n): return int("".join(k for k, g in groupby(bin(n)[2:])), 2)
print([a(n) for n in range(84)]) # Michael S. Branicky, Jul 23 2022

Crossrefs

Cf. A007088, A090077, A090078, A090080.

Cf. A030308, A005811.

Sequence in context: A068822 A351517 A337224 * A165195 A121487 A057031

Adjacent sequences: A090076 A090077 A090078 * A090080 A090081 A090082

Keyword

nonn,base

Author

Reinhard Zumkeller, Nov 20 2003

Status

approved