A135521 a(n) = 2^(A091090(n)) - 1.

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

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

G.f. A(x) satisfies: A(x) = x/(1 - x) + 2*x*A(x^2). - Ilya Gutkovskiy, Dec 18 2019

Example

From Omar E. Pol, Mar 11 2011: (Start)
Can be written as a triangle with 2^k entries on each row:
1,
1,3,
1,3,1,7,
1,3,1,7,1,3,1,15,
1,3,1,7,1,3,1,15,1,3,1,7,1,3,1,31,
1,3,1,7,1,3,1,15,1,3,1,7,1,3,1,31,1,3,1,7,1,3,1,15,1,3, 1,7,1,3,1,63,
Last term of rows are 2^(k+1) - 1. It appears that the row sums give A001787.
(End)

Maple

GS(2, 6, 200); [see A135416].
# Input n is the number of rows.
A135521_list := proc(n) local i, k, NimSum;
NimSum := proc(a, b) option remember; local i;
zip((x, y)->`if`(x<>y, 1, 0), convert(a, base, 2), convert(b, base, 2), 0);
add(`if`(%[i]=1, 2^(i-1), 0), i=1..nops(%)) end:
seq(seq(NimSum(i, i+1), i=0..2^k-1), k=0..n) end:
A135521_list(5); # Peter Luschny, May 31 2011

Mathematica

Flatten[Table[BitXor[i, i + 1], {k, 0, 10}, {i, 0, -1 + 2^k}]] (* Peter Luschny, May 31 2011 *)

Prog

(PARI)
A091090(n) = { my(m=valuation(n+1, 2)); if(n>>m, m+1, max(m, 1)); }; \\ From A091090
A135521(n) = ((2^A091090(n))-1); \\ Antti Karttunen, Sep 27 2018

Crossrefs

Cf. A135416, A091090.

This is Guy Steele's sequence GS(2, 6) (see A135416).

Cf. A000225, A001787. - Omar E. Pol, Mar 11 2011

Sequence in context: A361519 A236757 A095250 * A344763 A176032 A218403

Adjacent sequences: A135518 A135519 A135520 * A135522 A135523 A135524

Keyword

nonn,tabf

Author

N. J. A. Sloane, based on a message from Guy Steele and Don Knuth, Mar 01 2008

Status

approved