

A004641


Fixed under 0 > 10, 1 > 100.


9



1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1
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OFFSET

1,1


COMMENTS

Partial sums: A088462.  Reinhard Zumkeller, Dec 05 2009
Write w(n) = a(n) for n >= 1. Each w(n) is generated by w(i) for exactly one i <= n; let g(n) = i. Each w(i) generates a single 1, in a word (10 or 100) that starts with 1. Therefore, g(n) is the number of 1s among w(1), ..., w(n), so that g = A088462. That is, this sequence is generated by its partial sums.  Clark Kimberling, May 25 2011


LINKS

T. D. Noe, Table of n, a(n) for n = 1..8119
Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), arXiv:1710.01498 [math.NT], 2017.
Wieb Bosma, Michel Dekking, Wolfgang Steiner, A remarkable sequence related to Pi and sqrt(2), Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A4.
N. G. de Bruijn, Sequences of zeros and ones generated by special production rules, Nederl. Akad. Wetensch. Indag. Math. 43 (1981), no. 1, 2737. Reprinted in Physics of Quasicrystals, ed. P. J. Steinhardt et al., p. 664.
C. J. Glasby, S. P. Glasby, F. Pleijel, Worms by number, Proc. Roy. Soc. B, Proc. Biol. Sci. 275 (1647) (2008) 20712076.
Index entries for characteristic functions


FORMULA

a(n) = floor(n*(sqrt(2)  1) + sqrt(1/2))  floor((n  1)*(sqrt(2)  1) + sqrt(1/2)) (from the de Bruijn reference).  Peter J. Taylor, Mar 26 2015
From Jianing Song, Jan 02 2019: (Start)
a(n) = A001030(n)  1.
a(n) = A006337(n9)  1 = A159684(n10) for n >= 10. (End)


MAPLE

P(0):= (1, 0): P(1):= (1, 0, 0):
((P~)@@6)([1]);
# in Maple 12 or earlier, comment the above line and uncomment the following:
# (curry(map, P)@@6)([1]); # Robert Israel, Mar 26 2015


MATHEMATICA

Nest[ Flatten[# /. {0 > {1, 0}, 1 > {1, 0, 0}}] &, {1}, 5] (* Robert G. Wilson v, May 25 2011 *)


PROG

(MAGMA) [Floor(n*(Sqrt(2)  1) + Sqrt(1/2))  Floor((n  1)*(Sqrt(2)  1) + Sqrt(1/2)): n in [0..100]]; // Vincenzo Librandi, Mar 27 2015


CROSSREFS

Equals A001030  1. Essentially the same as A006337  1 and A159684.
Characteristic function of A086377.
Cf. A081477.
Sequence in context: A189298 A288375 A121559 * A266441 A266672 A266070
Adjacent sequences: A004638 A004639 A004640 * A004642 A004643 A004644


KEYWORD

nonn,nice,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



