|
| |
|
|
A001468
|
|
There are a(n) 2's between successive 1's.
(Formerly M0099 N0036)
|
|
21
|
|
|
|
1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
The Fibonacci word on the alphabet {2,1}, with an extra 1 in front. - Michel Dekking, Nov 26 2018
Start with 1, apply 1->12, 2->122, take limit. - Philippe Deléham, Sep 23 2005
Also number of occurrences of n in Hofstadter G-sequence (A005206) and in A019446. - Reinhard Zumkeller, Feb 02 2012, Aug 07 2011
A block-fractal sequence: every block occurs infinitely many times. Also a reverse block-fractal sequence. See A280511. - Clark Kimberling, Jan 06 2017
|
|
|
REFERENCES
|
D. Gault and M. Clint, "Curiouser and curiouser" said Alice. Further reflections on an interesting recursive function, Internat. J. Computer Math., 26 (1988), 35-43. See Table 2.
D. R. Hofstadter, personal communication, Jul 15 1977.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
|
LINKS
|
Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151.
D. Gault and M. Clint, "Curiouser and curiouser" said Alice. Further reflections on an interesting recursive function, Internat. J. Computer Math., 26 (1988), 35-43.
D. Gault & M. Clint, "Curiouser and curiouser said Alice. Further reflections on an interesting recursive function, Intern. J. Computer. Math., 26 (1988), 35-43. (Annotated scanned copy)
D. R. Hofstadter, Eta-Lore [Cached copy, with permission]
D. R. Hofstadter, Pi-Mu Sequences [Cached copy, with permission]
D. R. Hofstadter and N. J. A. Sloane, Correspondence, 1977 and 1991 [See DRH latter, p. 2, Eq. (2), the sequence marked A006336, which is now A001468].
J. V. Pennington and T. F. Mulcrone, Problem E1226, Amer. Math. Monthly, 64 (1957), 197-198.
Leon Recht, Martin Rosenbaum and E. P. Starke, Problem 4247, Amer. Math. Monthly, 55 (1948), 588-592.
N. J. A. Sloane, Handwritten notes on Self-Generating Sequences, 1970 (note that A1148 has now become A005282)
|
|
|
FORMULA
|
a(n) = [(n+1) tau] - [n tau], tau = (1 + sqrt 5)/2 = A001622, [] = floor function.
a(n) = A000201(n+1) - A000201(n) = A022342(n+1) - A022342(n), n >= 1; i.e., the first term discarded, this yields the first differences of A000201 and A022342. - M. F. Hasler, Oct 13 2017
|
|
|
MAPLE
|
Digits := 100: t := evalf( (1+sqrt(5))/2); A001468 := n-> floor((n+1)*t)-floor(n*t);
|
|
|
MATHEMATICA
|
Table[Floor[GoldenRatio*(n + 1)] - Floor[GoldenRatio*n], {n, 0, 80}] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006 *)
Nest[ Flatten[# /. {1 -> {1, 2}, 2 -> {1, 2, 2}}] &, {1}, 6] (* Robert G. Wilson v, May 20 2014 and corrected Apr 24 2017 following Clark Kimberling's email of Mar 22 2017 *)
|
|
|
PROG
|
(Haskell)
import Data.List (group)
a001468 n = a001468_list !! n
a001468_list = map length $ group a005206_list
-- Reinhard Zumkeller, Aug 07 2011
(PARI) a=[1]; for(i=1, 30, a=concat([a, vector(a[i], j, 2), 1])); a \\ Or compute as A001468(n)=A201(n+1)-A201(n) with A201(n)=(n+sqrtint(5*n^2))\2, working for n>=0 although A000201 is defined for n>=1. - M. F. Hasler, Oct 13 2017
|
|
|
CROSSREFS
|
Same as A014675 if initial 1 is deleted. Cf. A003849, A000201, A280511.
Sequence in context: A080634 A109925 A180227 * A014675 A107362 A166332
Adjacent sequences: A001465 A001466 A001467 * A001469 A001470 A001471
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
Rechecked by N. J. A. Sloane, Nov 07 2001
|
|
|
STATUS
|
approved
|
| |
|
|
