A103842 - OEIS

%I #15 Feb 06 2022 14:49:54

%S 1,1,0,1,0,1,1,1,0,0,1,1,0,1,1,1,1,1,0,1,0,1,1,1,1,0,0,1,1,1,1,1,1,0,

%T 0,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,1,1,1,1,0,1,0,1,1,1,

%U 1,1,1,1,1,1,0,1,0,0,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,0

%N Triangle read by rows: row n is binary expansion of 2^n-n, n >= 1.

%C This sequence can also be obtained by reading (from bottom to top, column by column) the array given in A103582 after suppressing the terms below the main diagonal.

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [<a href="http://neilsloane.com/doc/slopey.pdf">pdf</a>, <a href="http://neilsloane.com/doc/slopey.ps">ps</a>].

%H David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL8/Sloane/sloane300.html">Sloping binary numbers: a new sequence related to the binary numbers</a>, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

%e Table begins:

%e 1

%e 1 0

%e 1 0 1

%e 1 1 0 0

%e 1 1 0 1 1

%e 1 1 1 0 1 0

%e 1 1 1 1 0 0 1

%p p:=proc(n) local A,j,b: A:=convert(2^n-n,base,2): for j from 1 to nops(A) do b:=j->A[nops(A)+1-j] od: seq(b(j),j=1..nops(A)): end: for n from 1 to 15 do p(n) od; # yields sequence in triangular form # _Emeric Deutsch_, Apr 16 2005

%t Table[IntegerDigits[2^n-n,2],{n,20}]//Flatten (* _Harvey P. Dale_, Feb 06 2022 *)

%o (PARI) tabl(nn) = for (n=1, nn, print(binary(2^n-n))); \\ _Michel Marcus_, Mar 01 2015

%Y Cf. A000325, A103582.

%K nonn,tabl,easy

%O 1,1

%A _Philippe Deléham_, Mar 31 2005

%E More terms from _Emeric Deutsch_, Apr 16 2005