(Translated by https://www.hiragana.jp/)
# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a001468 Showing 1-1 of 1 %I A001468 M0099 N0036 #102 Aug 26 2022 10:26:17 %S A001468 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, %T A001468 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, %U A001468 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 %N A001468 There are a(n) 2's between successive 1's. %C A001468 The Fibonacci word on the alphabet {2,1}, with an extra 1 in front. - _Michel Dekking_, Nov 26 2018 %C A001468 Start with 1, apply 1->12, 2->122, take limit. - _Philippe Deléham_, Sep 23 2005 %C A001468 Also number of occurrences of n in Hofstadter G-sequence (A005206) and in A019446. - _Reinhard Zumkeller_, Feb 02 2012, Aug 07 2011 %C A001468 A block-fractal sequence: every block occurs infinitely many times. Also a reverse block-fractal sequence. See A280511. - _Clark Kimberling_, Jan 06 2017 %D A001468 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 A001468 D. R. Hofstadter, personal communication, Jul 15 1977. %D A001468 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). %D A001468 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A001468 Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 %H A001468 M. Bunder and K. Tognetti, On the self matching properties of [j tau], Discrete Math., 241 (2001), 139-151. %H A001468 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. %H A001468 D. Gault and 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) %H A001468 D. R. Hofstadter, Eta-Lore [Cached copy, with permission] %H A001468 D. R. Hofstadter, Pi-Mu Sequences [Cached copy, with permission] %H A001468 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]. %H A001468 J. V. Pennington and T. F. Mulcrone, Problem E1226, Amer. Math. Monthly, 64 (1957), 197-198. %H A001468 Leon Recht, Martin Rosenbaum and E. P. Starke, Problem 4247, Amer. Math. Monthly, 55 (1948), 588-592. %H A001468 N. J. A. Sloane, Handwritten notes on Self-Generating Sequences, 1970 (note that A1148 has now become A005282) %H A001468 N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence) %F A001468 a(n) = [(n+1) tau] - [n tau], tau = (1 + sqrt 5)/2 = A001622, [] = floor function. %F A001468 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 %p A001468 Digits := 100: t := evalf( (1+sqrt(5))/2); A001468 := n-> floor((n+1)*t)-floor(n*t); %t A001468 Table[Floor[GoldenRatio*(n + 1)] - Floor[GoldenRatio*n], {n, 0, 80}] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 14 2006 *) %t A001468 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 *) %t A001468 SubstitutionSystem[{1->{1,2},2->{1,2,2}},{1},{6}][[1]] (* _Harvey P. Dale_, Jan 31 2022 *) %o A001468 (Haskell) %o A001468 import Data.List (group) %o A001468 a001468 n = a001468_list !! n %o A001468 a001468_list = map length $ group a005206_list %o A001468 -- _Reinhard Zumkeller_, Aug 07 2011 %o A001468 (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 %o A001468 (Python) %o A001468 def A001468(length): %o A001468 a = [1] %o A001468 for i in range(length): %o A001468 for _ in range(a[i]): %o A001468 a.append(2) %o A001468 a.append(1) %o A001468 if len(a)>=length: %o A001468 break %o A001468 return a[:length] # _Nicholas Stefan Georgescu_, Jun 02 2022 %o A001468 (Python) %o A001468 from math import isqrt %o A001468 def A001468(n): return (n+1+isqrt(m:=5*(n+1)**2)>>1)-(n+isqrt(m-10*n-5)>>1) # _Chai Wah Wu_, Aug 25 2022 %Y A001468 Same as A014675 if initial 1 is deleted. Cf. A003849, A000201, A280511. %Y A001468 The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A000201 as the parent: A000201, A001030, A001468, A001950, A003622, A003842, A003849, A004641, A005614, A014675, A022342, A088462, A096270, A114986, A124841. - _N. J. A. Sloane_, Mar 11 2021 %K A001468 nonn,easy,nice %O A001468 0,2 %A A001468 _N. J. A. Sloane_ %E A001468 Rechecked by _N. J. A. Sloane_, Nov 07 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE