

A164677


For a binary reflected Gray code, the (Hamming/Euclidean) distance between 2 subsequent points x and y is 1, say in coordinate k. If y has a 1 in coordinate k and x has a 0, than (x,y) is indicated by k, if it is the other way around, (x,y) is indicated by k. The sequence has a fractal character such that G(d+1) = G(d) d+1 R(G(d)) where R(G(d)) alters d > d and leaves all other numbers invariant.


4



1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5
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OFFSET

1,2


COMMENTS

This is the paperfolding sequence Fold(1,2,3,4,5,...). It is also the fixed point of the map 1>1,2; 2>1,3; 3>1,4; 4>1,5; ...; 1>1,2; 2>1,3; 3>1,4; 4>1,5; ... [Allouche and Shallit].  N. J. A. Sloane, Jul 27 2012
Multiplicative because both A034947 and A001511 are.  Andrew Howroyd, Aug 06 2018


REFERENCES

J.P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 203, Exercise 15.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..8192
Index entries for sequences obtained by enumerating foldings


FORMULA

a(n) = (1)^chi_A091067(n)*A001511(n), where chi_A091067 is the characteristic function of A091067.  M. F. Hasler, Aug 06 2015
a(n) = A034947(n)*A001511(n).  Andrew Howroyd, Aug 06 2018


PROG

(PARI) A164677(n)=(valuation(n, 2)+1)*if(n>>valuation(n, 2)%4==3, 1, 1) \\ M. F. Hasler, Aug 06 2015


CROSSREFS

Absolute values give A001511.
Indices of negative terms are listed in A091067.  M. F. Hasler, Aug 06 2015
Cf. A034947.
Sequence in context: A187808 A317673 A317954 * A001511 A265331 A244569
Adjacent sequences: A164674 A164675 A164676 * A164678 A164679 A164680


KEYWORD

easy,sign,mult


AUTHOR

Arie Bos, Aug 20 2009


EXTENSIONS

More terms from Alois P. Heinz, Jan 30 2012


STATUS

approved



