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

Author

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

Keywords

• nonn
• tabf

Examples

			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)
		

Links

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

Crossrefs

Cf. A135416, A091090.

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

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

Programs

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 *)

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

Formula

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