A090050 Numbers having equal length of longest contiguous block of zeros and ones in binary expansion.

2, 5, 10, 12, 19, 21, 25, 38, 42, 44, 50, 51, 52, 56, 71, 75, 76, 77, 83, 85, 89, 100, 101, 102, 105, 108, 113, 142, 147, 150, 153, 154, 155, 166, 170, 172, 178, 179, 180, 184, 199, 201, 202, 203, 204, 205, 210, 211, 212, 217, 226, 227, 232, 240, 271, 279, 284

Offset: 1

Author

Reinhard Zumkeller, Nov 20 2003

Keywords

• nonn
• base

Comments

A087117(a(n)) = A038374(a(n)), see also A000975.

Examples

			180 -> '10110100' with A087117(180)=2 and A038374(180)=2, therefore 180 is a term.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A031443 (binary digitally balanced).

Cf. A000975, A038374, A087117.

Programs

Haskell

a090050 n = a090050_list !! (n+1)
a090050_list = [x | x <- [1..], a087117 x == a038374 x]
-- Reinhard Zumkeller, May 01 2012

Mathematica

zobQ[n_]:=Module[{s=Split[IntegerDigits[n,2]]},Max[Length/@Select[ s, MemberQ[ #,0]&]] == Max[Length/@Select[s,MemberQ[#,1]&]]]; Select[ Range[ 300],zobQ] (* Harvey P. Dale, Aug 25 2019 *)
Select[Range@1000, (s=Split@IntegerDigits[#,2]; Length@s>1 && Last@Differences@(Length@# & /@ Union@s) == 0) &] (* Hans Rudolf Widmer, Oct 10 2023 *)

Extensions

Definition corrected, thanks to Leroy Quet. - Sep 17 2008