cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A092323 #29 Aug 18 2025 11:46:52
%S A092323 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,
%T A092323 15,15,15,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,
%U A092323 31,31,31,31,31,31,31,31,31,31,31,31,63,63,63,63,63,63,63,63,63,63,63
%N A092323 2^m - 1 appears 2^m times.
%C A092323 Or, write n in binary and change the most significant bit to 0 and all other bits to 1.
%C A092323 a(n) = A053644(n) - 1 = A003817(n) - A053644(n).
%C A092323 a(n) = floor(A003817(n-1)/2). [_Reinhard Zumkeller_, Jul 18 2010]
%F A092323 a(n) = if n=1 then 0 else a(floor(n/2))*2 + 1.
%F A092323 a(1)=0, a(2n) = 2*a(n)+1, a(2n+1) = a(2n). - _Ralf Stephan_, Nov 18 2010
%t A092323 Table[FromDigits[#, 2] &@ Table[1, {IntegerLength[n, 2] - 1}], {n, 80}] (* _Michael De Vlieger_, Jun 26 2016 *)
%t A092323 Table[Table[2^m-1,2^m],{m,0,6}]//Flatten (* _Harvey P. Dale_, May 22 2021 *)
%t A092323 Table[PadRight[{},2^m,2^m-1],{m,0,6}]//Flatten (* _Harvey P. Dale_, Aug 18 2025 *)
%o A092323 (Magma) [n le 2 select n-1 else Self(Floor(n/2))*2+1: n in [1..100]]; // _Vincenzo Librandi_, Jun 27 2016
%Y A092323 Cf. A003817, A053644.
%K A092323 nonn,easy
%O A092323 1,4
%A A092323 _Reinhard Zumkeller_, Feb 15 2004