A092323 2^m - 1 appears 2^m times.

0, 1, 1, 3, 3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 7, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63

Offset: 1

Author

Reinhard Zumkeller, Feb 15 2004

Keywords

• nonn
• easy

Comments

Or, write n in binary and change the most significant bit to 0 and all other bits to 1.

a(n) = A053644(n) - 1 = A003817(n) - A053644(n).

a(n) = floor(A003817(n-1)/2). [Reinhard Zumkeller, Jul 18 2010]

Crossrefs

Cf. A003817, A053644.

Programs

Magma

[n le 2 select n-1 else Self(Floor(n/2))*2+1: n in [1..100]]; // Vincenzo Librandi, Jun 27 2016

Mathematica

Table[FromDigits[#, 2] &@ Table[1, {IntegerLength[n, 2] - 1}], {n, 80}] (* Michael De Vlieger, Jun 26 2016 *)
Table[Table[2^m-1,2^m],{m,0,6}]//Flatten (* Harvey P. Dale, May 22 2021 *)
Table[PadRight[{},2^m,2^m-1],{m,0,6}]//Flatten (* Harvey P. Dale, Aug 18 2025 *)

Formula

a(n) = if n=1 then 0 else a(floor(n/2))*2 + 1.

a(1)=0, a(2n) = 2*a(n)+1, a(2n+1) = a(2n). - Ralf Stephan, Nov 18 2010