A005375 -id:A005375 - cp's OEIS frontend

A005185 Hofstadter Q-sequence: a(1) = a(2) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 2.

1, 1, 2, 3, 3, 4, 5, 5, 6, 6, 6, 8, 8, 8, 10, 9, 10, 11, 11, 12, 12, 12, 12, 16, 14, 14, 16, 16, 16, 16, 20, 17, 17, 20, 21, 19, 20, 22, 21, 22, 23, 23, 24, 24, 24, 24, 24, 32, 24, 25, 30, 28, 26, 30, 30, 28, 32, 30, 32, 32, 32, 32, 40, 33, 31, 38, 35, 33, 39, 40, 37, 38, 40, 39

Offset: 1

Simon Plouffe and N. J. A. Sloane, May 20 1991

Rate of growth is not known. In fact it is not even known if this sequence is defined for all positive n.
Roman Pearce, Aug 29 2014, has computed that a(n) exists for n <= 10^10. - N. J. A. Sloane
a(n) exists for n <= 3*10^10. - M. Eric Carr, Jul 02 2023

			a(18) = 11 because a(17) is 10 and a(16) is 9, so we take a(18 - 10) + a(18 - 9) = a(8) + a(9) = 5 + 6 = 11.

B. W. Conolly, "Meta-Fibonacci sequences," in S. Vajda, editor, Fibonacci and Lucas Numbers and the Golden Section. Halstead Press, NY, 1989, pp. 127-138.
R. K. Guy, Unsolved Problems in Number Theory, Sect. E31.
D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 138.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. Vajda, Fibonacci and Lucas Numbers and the Golden Section, Wiley, 1989, see p. 129.
S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 129.

T. D. Noe and N. J. A. Sloane, Table of n, a(n) for n = 1..10000
Altug Alkan, On a conjecture about generalized Q-recurrence, Open Mathematics, Vol. 16 (2018), pp. 1490-1500.
Altug Alkan, On a Generalization of Hofstadter's Q-Sequence: A Family of Chaotic Generational Structures, Complexity (2018) Article ID 8517125.
Altug Alkan, Nathan Fox, and Orhan Ozgur Aybar, On Hofstadter Heart Sequences, Complexity, 2017.
B. Balamohan, A. Kuznetsov, and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, J. Integer Sequences, Vol. 10 (2007), #07.7.1.
Thomas Bloom, Problem 422, Erdős Problems.
Paul Bourke, Hofstadter "Q" Series.
Paul Bourke, Hofstadter "Q" Series. [Cached copy, pdf only, with permission]
Paul Bourke, Listen to first 300 terms of this sequence. [Cached copy from the Hofstadter "Q" web page, with permission]
Joseph Callaghan, John J. Chew III, and Stephen M. Tanny, On the behavior of a family of meta-Fibonacci sequences, SIAM Journal on Discrete Mathematics 18.4 (2005): 794-824. See p. 794.
Benoit Cloitre, Plot of a(n)/n - 1/2 for n=1 up to 2^19.
J.-P. Davalan, Douglas Hofstadter's sequences.
Jonathan H. B. Deane and Guido Gentile, A diluted version of the problem of the existence of the Hofstadter sequence, arXiv:2311.13854 [math.NT], 2023.
Nathaniel D. Emerson, A Family of Meta-Fibonacci Sequences Defined by Variable-Order Recursions, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.8.
Nathan Fox, Linear-Recurrent Solutions to Meta-Fibonacci Recurrences, Part 1 (video), Rutgers Experimental Math Seminar, Oct 01 2015. Part 2 is vimeo.com/141111991.
Nathan Fox, Finding Linear-Recurrent Solutions to Hofstadter-Like Recurrences Using Symbolic Computation, arXiv:1609.06342 [math.NT], 2016.
Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv:1611.08244 [math.NT], 2016.
Nathan Fox, A New Approach to the Hofstadter Q-Recurrence, arXiv:1807.01365 [math.NT], 2018.
S. W. Golomb, Discrete chaos: sequences satisfying "strange" recursions, unpublished manuscript, circa 1990 [cached copy, with permission (annotated)].
J. Grytczuk, Another variation on Conway's recursive sequence, Discr. Math. 282 (2004), 149-161.
R. K. Guy, Letter to N. J. A. Sloane, Sep 25 1986.
R. K. Guy, Some suspiciously simple sequences, Amer. Math. Monthly 93 (1986), 186-190; 94 (1987), 965; 96 (1989), 905.
Nick Hobson, Python program for this sequence.
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.
D. R. Hofstadter, Curious patterns and non-patterns in a family of meta-Fibonacci recursions, Lecture in Doron Zeilberger's Experimental Mathematics Seminar, Rutgers University, April 10 2014; Part 1, Part 2.
D. R. Hofstadter, Plot of first 100 million terms.
Abraham Isgur, Mustazee Rahman, and Stephen Tanny, Solving non-homogeneous nested recursions using trees, Annals of Combinatorics 17.4 (2013): 695-710. See p. 695. - _N. J. A. Sloane_, Apr 16 2014
A. Isgur, R. Lech, S. Moore, S. Tanny, Y. Verberne, and Y. Zhang, Constructing New Families of Nested Recursions with Slow Solutions, SIAM J. Discrete Math., 30(2), 2016, 1128-1147. (20 pages); DOI:10.1137/15M1040505.
Piotr Miska, Bartosz Sobolewski, and Maciej Ulas, Binary sequences meet the Fibonacci sequence, arXiv:2412.11319 [math.NT], 2024. See p. 20.
K. Pinn, Order and chaos in Hofstadter's Q(n) sequence, Complexity, 4:3 (1999), 41-46.
K. Pinn, A chaotic cousin of Conway's recursive sequence, Experimental Mathematics, 9:1 (2000), 55-65.
K. Pinn, A Chaotic Cousin Of Conway's Recursive Sequence, arXiv:cond-mat/9808031 [cond-mat.stat-mech], 1998.
N. J. A. Sloane and Brady Haran, Amazing Graphs III, Numberphile video (2019).
I. Vardi, Email to N. J. A. Sloane, Jun. 1991.
A. M. M. Sharif Ullah, Surface Roughness Modeling Using Q-Sequence, Mathematical and Computational Applications, 2017.
Eric Weisstein's World of Mathematics, Hofstadter's Q-Sequence.
Wikipedia, Hofstadter sequence.
Pedro Zanetti, C++ code snippet for this sequence.
Index entries for sequences from "Goedel, Escher, Bach"
Index entries for Hofstadter-type sequences

Cf. A004001, A005206, A005374, A005375, A005378.
Cf. A005379, A070867, A226222, A239913, A284019.
Cf. A081827 (first differences).
Cf. A226244, A226245 (record values and where they occur).
See A244477 for a different start.

#include 
#define LIM 20
int Qa[LIM];
int Q(int n){if (n==1 || n==2){return 1;} else{return Qa[n-Qa[n-1]]+Qa[n-Qa[n-2]];}}
int main(){int i;printf("n\tQ\n");for(i=1; iGonzalo Ciruelos, Aug 01 2013

a005185 n = a005185_list !! (n-1)
a005185_list = 1 : 1 : zipWith (+)
   (map a005185 $ zipWith (-) [3..] a005185_list)
   (map a005185 $ zipWith (-) [3..] $ tail a005185_list)
-- Reinhard Zumkeller, Jun 02 2013, Sep 15 2011

I:=[1,1]; [n le 2 select I[n] else Self(n-Self(n-1))+Self(n-Self(n-2)): n in [1..90]]; // Vincenzo Librandi, Aug 08 2014

A005185 := proc(n) option remember;
    if n<=2 then 1
    elif n > procname(n-1) and n > procname(n-2) then
        RETURN(procname(n-procname(n-1))+procname(n-procname(n-2)));
    else
        ERROR(" died at n= ", n);
    fi; end proc;
# More generally, the following defines the Hofstadter-Huber sequence Q(r,s) - N. J. A. Sloane, Apr 15 2014
r:=1; s:=2;
a:=proc(n) option remember; global r,s;
if n <= s then  1
else
    if (a(n-r) <= n) and (a(n-s) <= n) then
    a(n-a(n-r))+a(n-a(n-s));
    else lprint("died with n =",n); return (-1);
    fi; fi; end;
[seq(a(n), n=1..100)];

a[1]=a[2]=1; a[n_]:= a[n]= a[n -a[n-1]] + a[n -a[n-2]]; Table[ a[n], {n,70}]

q:=proc(n) option remember; begin if n<=2 then 1 else q(n-q(n-1))+q(n-q(n-2)) end_if; end_proc: q(i)$i=1..100; // Zerinvary Lajos, Apr 03 2007

{a(n)= local(A); if(n<1, 0, A=vector(n,k,1); for(k=3, n, A[k]= A[k-A[k-1]]+ A[k-A[k-2]]); A[n])} /* Michael Somos, Jul 16 2007 */

from functools import lru_cache
@lru_cache(maxsize=None)
def a(n):
    if n < 3: return 1
    return a(n - a(n-1)) + a(n - a(n-2))
print([a(n) for n in range(1, 75)]) # Michael S. Branicky, Jul 26 2021

@CachedFunction
def a(n):
    if (n<3): return 1
    else: return a(n -a(n-1)) + a(n -a(n-2))
[a(n) for n in (1..70)] # G. C. Greubel, Feb 13 2020

(define q (lambda (n) (cond ( (eqv? n 0) 1) ( (eqv? n 1) 1) ( #t (+ (q (- n (q (- n 1)))) (q (- n (q (- n 2)))))))))

;; An implementation of memoization-macro definec can be found for example in: http://oeis.org/wiki/Memoization
(definec (A005185 n) (if (<= n 2) 1 (+ (A005185 (- n (A005185 (- n 1)))) (A005185 (- n (A005185 (- n 2)))))))
;; Antti Karttunen, Mar 22 2017

A005374 Hofstadter H-sequence: a(n) = n - a(a(a(n-1))).

Original entry on oeis.org

0, 1, 1, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 19, 20, 20, 21, 22, 23, 23, 24, 24, 25, 26, 26, 27, 28, 29, 29, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 41, 41, 42, 42, 43, 44, 45, 45, 46, 46, 47, 48, 48, 49, 50

Offset: 0

N. J. A. Sloane

Rule for constructing the sequence: a(n) = An, where An denotes the Lamé antecessor to (or right shift of) n, which is found by replacing each Lm(i) in the Zeckendorffian expansion (obtained by repeatedly subtracting the largest Lamé number (A000930) you can until nothing remains) by Lm(i-1) (A1=1). For example: 58 = 41 + 13 + 4, so a(58)= 28 + 9 + 3 = 40.
From Albert Neumueller (albert.neu(AT)gmail.com), Sep 28 2006: (Start)
As is shown on page 137 of Goedel, Escher, Bach, a recursively built tree structure can be obtained from this sequence:
  20.21..22..23.24.25.26.27.28
  .\./.../.../...\./...\./../
  ..14.15..16....17....18..19
  ...\./.../..../.......\./
  ....10.11...12........13
  .....\./.../........./
  ......7...8........9.
  .......\./......./
  ........5......6
  .........\.../
  ...........4
  ........../
  .........3
  ......../
  .......2
  ....\./
  .....1
To construct the tree: node n is connected to the node a(n) below it:
  ...n
  ../
  a(n)
For example:
  ...8
  ../
  .5
since a(8) = 5. If the nodes of the tree are read from bottom-to-top, left-to-right, we obtain the natural numbers: 1, 2, 3, 4, 5, 6, ...
The tree has a recursive structure, since the following construct
  ....../
  .....x
  ..../
  ...x
  \./
  .x
can be repeatedly added on top of its own ends, to construct the tree from its root: E.g.,
  ................../
  .................x
  ................/
  ...............x
  ......../...\./
  .......x.....x
  ....../...../
  .....x.....x
  ..\./...../
  ...x.....x
  ....\.../
  ......x
(End)
From Pierre Letouzey, Feb 20 2025: (Start)
For all n >= 0, A005206(n) <= a(n) <= A005375(n), as proved in Letouzey-Li-Steiner link. Last equality A005206(n) = a(n) occurs at n = 12; last equality a(n) = A005375(n) occurs at n = 18.
For all n >= 0, |a(n)-c*n| < 0.996, where c is the real root of x^3 + x - 1 = 0, c = 0.682327803828019327369483739... Proved in Letouzey link. (End)
The bound for |a(n)-c*n| is improved to 0.862 in Shallit (2025). - Jeffrey Shallit, Mar 09 2025

D. R. Hofstadter, Goedel, Escher, Bach: an Eternal Golden Braid, Random House, 1980, p. 137.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Benoit Cloitre, Plot of a(n)-c*n where c=0.6823278...
Larry Ericksen and Peter G. Anderson, Patterns in differences between rows in k-Zeckendorf arrays, The Fibonacci Quarterly, Vol. 50, No. 1 (February 2012), pp. 11-18.
Nick Hobson, Python program for this sequence
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
Pierre Letouzey, S. Li and W. Steiner, Pointwise order of generalized Hofstadter functions G,H and beyond, arXiv:2410.00529 [cs.DM], 2024.
Pierre Letouzey, Generalized Hofstadter functions G,H and beyond: numeration systems and discrepancy arXiv:2502.12615 [cs.DM], 2025.
Programming Puzzles & Code Golf Stack Exchange, Hofstadter H-sequence
Jeffrey Shallit, The Narayana Morphism and Related Words, arXiv:2503.01026 [math.CO], 2025.
Eric Weisstein's World of Mathematics, Hofstadter H-Sequence
Wikipedia, Hofstadter sequence
Index entries for Hofstadter-type sequences
Index entries for sequences from "Goedel, Escher, Bach"

Cf. A202340, A202341, A202342.

a005374 n = a005374_list !! n
a005374_list = 0 : 1 : zipWith (-)
   [2..] (map (a005374 . a005374) $ tail a005374_list)
-- Reinhard Zumkeller, Dec 17 2011

A005374 := proc(n) option remember: if n<1 then 0 else n-A005374(A005374(A005374(n-1))) fi end: # Francisco Salinas (franciscodesalinas(AT)hotmail.com), Jan 06 2002
H:=proc(n) option remember; if n=1 then 1 else n-H(H(H(n-1))); fi; end proc;

a[n_]:= a[n]= n - a[a[a[n-1]]]; a[0] = 0; Table[a[n], {n, 0, 73}] (* Jean-François Alcover, Jul 28 2011 *)

first(m)=my(v=vector(m));v[1]=1;for(i=2,m,v[i]=i-v[v[v[i-1]]]);concat([0],v) \\ Anders Hellström, Dec 07 2015

@CachedFunction # a = A005374
def a(n): return 0 if (n==0) else n - a(a(a(n-1)))
[a(n) for n in range(101)] # G. C. Greubel, Nov 14 2022

Conjecture: a(n) = floor(c*n) + 0 or 1, where c is the real root of x^3+x-1 = 0, c=0.682327803828019327369483739... - Benoit Cloitre, Nov 05 2002 [Proved by Letouzey, see Letouzey link. - Pierre Letouzey, Feb 20 2025], [Also proved in Shallit (2025). - Jeffrey Shallit, Mar 09 2025]
a(n) = A020942(n) - 2*A064105(n) + A064106(n) (e.g. for n = 30 we get 20 = 93 - 2*137 + 201), and a(n) = 2*A020942(n) - A064105(n) - A023443(n) (e.g. for n = 30 we get 20 = 2*93 - 137 - 29). [Corrected by N. J. A. Sloane, Apr 29 2024 at the suggestion of A.H.M. Smeets.]
Also: a(n) = a(n-1) + 1 if n-1 belongs to sequence A064105-A020942-A000012, a(n-1) otherwise.
Recurrence: a(n) = a(n-1) if n-1 belongs to sequence A020942, a(n-1) + 1 otherwise.
Recurrence for n>=3: a(n) = Lm(k-1) + a(n-Lm(k)), where Lm(n) denotes Lamé sequence A000930(n) (Lm(n) = Lm(n-1) + Lm(n-3)) and k is such that Lm(k)< n <= Lm(k+1). Special case: a(Lm(n)) = Lm(n-1) for n>=1.
For n > 0: a(A136495(n)) = n. - Reinhard Zumkeller, Dec 17 2011

More terms from James Sellers, Jul 12 2000

Additional comments and formulas from Diego Torres (torresvillarroel(AT)hotmail.com), Nov 23 2002

A005376 a(n) = n - a(a(a(a(a(n-1))))).

Original entry on oeis.org

0, 1, 1, 2, 3, 4, 5, 6, 6, 7, 7, 8, 9, 9, 10, 11, 12, 12, 13, 14, 15, 16, 16, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 33, 34, 35, 35, 36, 37, 38, 39, 40, 40, 41, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 50, 51, 51, 52, 52, 53, 54, 54

Offset: 0

N. J. A. Sloane

nonn

Conjecture: a(n) is approximately c*n, where c is the real root of x^5+x-1 = 0, c=0.754877666246692760049508896... - Benoit Cloitre, Nov 05 2002
Rule for n-th term: a(n) = An, where An denotes the Lamé antecedent to (or right shift of) n, which is found by replacing each Lm(i) (Lm(n) = Lm(n-1) + Lm(n-5): A003520) in the Zeckendorffian expansion (obtained by repeatedly subtracting the largest Lamé number you can until nothing remains) with Lm(i-1) (A1=1). For example: 58 = 45 + 11 + 2, so a(58) = 34 + 8 + 1 = 43. - Diego Torres (torresvillarroel(AT)hotmail.com), Nov 24 2002
From Pierre Letouzey, Mar 06 2025: (Start)
For all n >= 0, A005375(n) <= a(n) <= A100721(n) as proved in Letouzey-Li-Steiner link. Last equality A005375(n) = a(n) for n = 25; last equality a(n) = A100721(n) for n = 33.
a(n) = c*n + O(ln(n)), with c conjectured by Benoit Cloitre above; see Letouzey link and Dilcher 1993. (End)

Karl Dilcher, On a class of iterative recurrence relations, in G. E. Bergum, A. N. Philippou, and A. F. Horadam, editors, Applications of Fibonacci Numbers, vol. 5, p. 143-158, Springer, 1993.
Douglas R. Hofstadter, "Goedel, Escher, Bach", p. 137.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

G. C. Greubel, Table of n, a(n) for n = 0..10000
Larry Ericksen and Peter G. Anderson, Patterns in differences between rows in k-Zeckendorf arrays, The Fibonacci Quarterly, Vol. 50, No. 1 (February 2012), pp. 11-18.
Nick Hobson, Python program for this sequence
Pierre Letouzey, Generalized Hofstadter functions G,H and beyond: numeration systems and discrepancy, arXiv:2502.12615 [cs.DM], 2025.
Pierre Letouzey, Shuo Li and Wolfgang Steiner, Pointwise order of generalized Hofstadter functions G,H and beyond, arXiv:2410.00529 [cs.DM], 2024.
Index entries for Hofstadter-type sequences
Index entries for sequences from "Goedel, Escher, Bach"

Cf. A005206, A005374, A005375, A100721.

H:=proc(n) option remember; if n=1 then 1 else n-H(H(H(H(H(n-1))))); fi; end proc;

a[n_]:= a[n]= If[n<1, 0, n -a[a[a[a[a[n-1]]]]]];
Table[a[n], {n, 0, 100}] (* G. C. Greubel, Nov 16 2022 *)

@CachedFunction # a = A005376
def a(n): return 0 if (n==0) else n - a(a(a(a(a(n-1)))))
[a(n) for n in range(101)] # G. C. Greubel, Nov 16 2022

a(n + a(a(a(a(n))))) = n (proved in Letouzey-Li-Steiner link). - Pierre Letouzey, Mar 06 2025

More terms from James Sellers, Jul 12 2000

A100721 a(n) = n - a(a(a(a(a(a(n-1)))))), a(0)=0.

Original entry on oeis.org

0, 1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31, 32, 33, 34, 34, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42, 42, 43, 44, 44, 45, 46, 47, 48, 49, 50, 50, 51, 51, 52, 53, 53, 54, 55, 56, 56, 57, 58, 59

Offset: 0

N. J. A. Sloane, Dec 12 2004

nonn

From Pierre Letouzey, Mar 06 2025: (Start)
For all n >= 0, A005376(n) <= a(n) as proved in Letouzey-Li-Steiner link. Last equality a(n) = A005376(n) for n = 33. Moreover a(n) <= b(n) for all sequences b also defined by b(0)=0 and then b(n)=n-b(...b(n-1)...) with more than 6 nested recursive calls.
a(n) = c*n + O(n^d), where c is the real root of x^6+x-1 = 0, c=0.7780895986786012... and d=0.1287... Proved in Letouzey link. See also Dilcher 1993. (End)

Karl Dilcher, On a class of iterative recurrence relations, in G. E. Bergum, A. N. Philippou, and A. F. Horadam, editors, Applications of Fibonacci Numbers, vol. 5, p. 143-158, Springer, 1993.

G. C. Greubel, Table of n, a(n) for n = 0..10000
Pierre Letouzey, Generalized Hofstadter functions G,H and beyond: numeration systems and discrepancy, arXiv:2502.12615 [cs.DM], 2025.
Pierre Letouzey, Shuo Li, and Wolfgang Steiner, Pointwise order of generalized Hofstadter functions G, H and beyond, arXiv:2410.00529 [cs.DM], 2024. See p. 1.

Cf. A005206, A005374, A005375, A005376.

H:=proc(n) option remember; if n=0 then 0 else n-H(H(H(H(H(H(n-1)))))); fi; end proc;

a[0]= 0; a[n_]:= a[n]= n - a[a[a[a[a[a[n-1]]]]]]; Table[ a[n], {n, 75}] (* Robert G. Wilson v, Dec 16 2004 *)

@CachedFunction # a = A100721
def a(n): return 0 if (n==0) else n - a(a(a(a(a(a(n-1))))))
[a(n) for n in range(1,100)] # G. C. Greubel, Nov 16 2022

a(n + a(a(a(a(a(n)))))) = n (proved in Letouzey-Li-Steiner link). - Pierre Letouzey, Mar 06 2025

a(0)=0 inserted by Pierre Letouzey, Mar 07 2025

Also first prepending column of the 4-Zeckendorf array (see Ericksen and Anderson).

N. J. A. Sloane observed already the relation between Hofstadter G/H-like sequences H_k and k-Zeckendorf arrays in May 2003, at least for k = 3 (see formula section and history of A005374). First observation most probably by Diego Torres, Nov 2002, relating the Hofstadter G/H-like sequences H_k with the k-Zeckendorf arrays and Lamé sequences of order k (see comments in A005375 and A005376).

Also first prepending column of the 5-Zeckendorf array (see Ericksen and Anderson).

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A194081 Smallest m such that A005375(m) = n.

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A372397 Numbers occurring exactly twice in Hofstadter G/H-like sequence H_4 (A005375).

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A005185 Hofstadter Q-sequence: a(1) = a(2) = 1; a(n) = a(n-a(n-1)) + a(n-a(n-2)) for n > 2.

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A005374 Hofstadter H-sequence: a(n) = n - a(a(a(n-1))).

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A005376 a(n) = n - a(a(a(a(a(n-1))))).

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A100721 a(n) = n - a(a(a(a(a(a(n-1)))))), a(0)=0.

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