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A059905 Index of first half of decomposition of integers into pairs based on A000695. 25
0, 1, 0, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 4, 5, 4, 5, 6, 7, 6, 7, 0, 1, 0, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 12, 13, 12, 13, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

One coordinate of a recursive non-self-intersecting walk on the square lattice Z^2.

LINKS

Peter Kagey, Table of n, a(n) for n = 0..8192

FORMULA

n = A000695(a(n)) + 2*A000695(A059906(n)).

To get a(n), write n as Sum b_j*2^j, then a(n) = Sum b_(2j)*2^j. - Vladimir Shevelev, Nov 13 2008

a(n) = Sum_{k>=0} A030308(n,k)*A077957(k). - Philippe Deléham, Oct 18 2011

G.f.: (1-x)^(-1) * Sum_{j>=0} 2^j*x^(2^j)/(1+x^(2^j)). - Robert Israel, Aug 12 2015

a(n) = A059906(2*n). - Velin Yanev, Dec 01 2016

EXAMPLE

A000695(a(14)) + 2*A000695(A059906(14)) = A000695(2) + 2*A000695(3) = 4 + 2*5 = 14.

If n=27, then b_0=1, b_1=1, b_2=0, b_3=1, b_4=1. Therefore a(n) = b_0 + b_2*2 + b_4*2^2 = 5. - Vladimir Shevelev, Nov 13 2008

MAPLE

f:= proc(n) local L; L:= convert(n, base, 2); add(L[2*i+1]*2^i, i=0..floor((nops(L)-1)/2)) end;

map(f, [$0..256]); # Robert Israel, Aug 12 2015

PROG

(Ruby)

def a(n)

  (0..n.bit_length/2).to_a.map { |i| (n >> 2 * i & 1) << i}.reduce(:+)

end # Peter Kagey, Aug 12 2015

(Python)

def a(n): return sum([(n>>2*i&1)<<i for i in xrange(int(len(bin(n)[2:])/2) + 1)])

print [a(n) for n in xrange(101)] # Indranil Ghosh, Jun 25 2017, after Ruby code by Peter Kagey

(PARI) A059905(n) = { my(t=1, s=0); while(n>0, s += (n%2)*t; n \= 4; t *= 2); (s); }; \\ Antti Karttunen, Apr 14 2018

CROSSREFS

Cf. A000695, A030308, A059906, A057300, A077957.

Sequence in context: A105436 A266911 A244075 * A295301 A014836 A197262

Adjacent sequences:  A059902 A059903 A059904 * A059906 A059907 A059908

KEYWORD

easy,nonn,look

AUTHOR

Marc LeBrun, Feb 07 2001

STATUS

approved

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Last modified December 9 22:04 EST 2018. Contains 318032 sequences. (Running on oeis4.)