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

1,1

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.

Links

Table of n, a(n) for n=1..105.

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000325, A103582.

Sequence in context: A248396 A285952 A371691 * A286064 A065535 A285518

Adjacent sequences: A103839 A103840 A103841 * A103843 A103844 A103845

Keyword

nonn,tabl,easy

Author

Philippe Deléham, Mar 31 2005

Extensions

More terms from Emeric Deutsch, Apr 16 2005

Status

approved