A103842 Triangle read by rows: row n is binary expansion of 2^n-n, n >= 1.

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, 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, 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

Offset: 1

Author

Philippe Deléham, Mar 31 2005

Keywords

• nonn
• tabl
• easy

Comments

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.

Examples

			Table begins:
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
		

Links

• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp.

Crossrefs

Cf. A000325, A103582.

Programs

Maple

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

Mathematica

Table[IntegerDigits[2^n-n,2],{n,20}]//Flatten (* Harvey P. Dale, Feb 06 2022 *)

PARI

tabl(nn) = for (n=1, nn, print(binary(2^n-n))); \\ Michel Marcus, Mar 01 2015

Extensions

More terms from Emeric Deutsch, Apr 16 2005