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A135521 a(n) = 2^(A091090(n)) - 1. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A281113 A236757 A095250 * A176032 A218403 A318506

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

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Last modified May 17 12:43 EDT 2021. Contains 343971 sequences. (Running on oeis4.)