A182105 -id:A182105 - cp's OEIS frontend

A215020 a(n) = log_2( A182105(n) ).

0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 4, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 4, 5, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 4, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 3, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1

Offset: 1

N. J. A. Sloane, Aug 01 2012

nonn

Apparently the leftmost positions of change with incrementing skew-binary numbers (A169683), see example. - Joerg Arndt, May 27 2016

Irregular table read by rows, where the k-th row counts from 0 up to the ruler function of k, A007814(k). - Allan C. Wechsler, Sep 26 2019

			From _Joerg Arndt_, May 27 2016: (Start)
The first nonnegative skew-binary numbers (dots denote zeros) are
n :  [skew-binary]  position of change
00:  [ . . . . . ]  -
01:  [ . . . . 1 ]  0
02:  [ . . . . 2 ]  0
03:  [ . . . 1 . ]  1
04:  [ . . . 1 1 ]  0
05:  [ . . . 1 2 ]  0
06:  [ . . . 2 . ]  1
07:  [ . . 1 . . ]  2
08:  [ . . 1 . 1 ]  0
09:  [ . . 1 . 2 ]  0
10:  [ . . 1 1 . ]  1
11:  [ . . 1 1 1 ]  0
12:  [ . . 1 1 2 ]  0
13:  [ . . 1 2 . ]  1
14:  [ . . 2 . . ]  2
15:  [ . 1 . . . ]  3
16:  [ . 1 . . 1 ]  0
17:  [ . 1 . . 2 ]  0
18:  [ . 1 . 1 . ]  1
19:  [ . 1 . 1 1 ]  0
20:  [ . 1 . 1 2 ]  0
21:  [ . 1 . 2 . ]  1
22:  [ . 1 1 . . ]  2
23:  [ . 1 1 . 1 ]  0
24:  [ . 1 1 . 2 ]  0
25:  [ . 1 1 1 . ]  1
26:  [ . 1 1 1 1 ]  0
27:  [ . 1 1 1 2 ]  0
28:  [ . 1 1 2 . ]  1
29:  [ . 1 2 . . ]  2
30:  [ . 2 . . . ]  3
31:  [ 1 . . . . ]  4
32:  [ 1 . . . 1 ]  0
33:  [ 1 . . . 2 ]  0
...
(End)
From _Allan C. Wechsler_, Sep 27 2019 (Start)
First few rows of irregular table derived from A007814 (see comments).
0
0 1
0
0 1 2
0
0 1
0
0 1 2 3
0
0 1
...
(End)

Wikipedia, Skew binary number system

Cf. A182105, A082850, A007814.

a(n) = A082850(n) - 1. - Omar E. Pol, Jun 18 2019

A133494 Diagonal of the array of iterated differences of A047848.

Original entry on oeis.org

1, 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329, 7625597484987, 22876792454961, 68630377364883

Offset: 0

Paul Barry, Paul Curtz, Dec 23 2007

a(n) is the number of ways to choose a composition C, and then choose a composition of each part of C. - Geoffrey Critzer, Mar 19 2012
a(n) is the top left entry of the n-th power of the 3 X 3 matrix [1, 1, 1; 1, 1, 1; 1, 1, 1]. - R. J. Mathar, Feb 03 2014
a(n) is the reptend length of 1/3^(n+1) in decimal. - Jianing Song, Nov 14 2018
Also the number of pairs of integer compositions, the first summing to n and the second with sum equal to the length of the first. If an integer composition is regarded as an arrow from sum to length, these are composable pairs, and the obvious composition operation founds a category of integer compositions. For example, we have (2,1,1,4) . (1,2,1) . (1,2) = (2,6), where dots represent the composition operation. The version without empty compositions is A000244. Composable triples are counted by 1 followed by A000302. The unordered version is A022811. - Gus Wiseman, Jul 14 2022

			From _Gus Wiseman_, Jul 15 2020: (Start)
The a(0) = 1 through a(3) = 9 ways to choose a composition of each part of a composition:
  ()  (1)  (2)      (3)
           (1,1)    (1,2)
           (1),(1)  (2,1)
                    (1,1,1)
                    (1),(2)
                    (2),(1)
                    (1),(1,1)
                    (1,1),(1)
                    (1),(1),(1)
(End)

G. C. Greubel, Table of n, a(n) for n = 0..1000
Bishal Deb, Cyclic sieving phenomena via combinatorics of continued fractions, arXiv:2508.13709 [math.CO], 2025. See p. 42.
Index entries for linear recurrences with constant coefficients, signature (3).

The strict version is A336139.
Splittings of partitions are A323583.
Multiset partitions of partitions are A001970.
Partitions of each part of a partition are A063834.
Compositions of each part of a partition are A075900.
Strict partitions of each part of a strict partition are A279785.
Compositions of each part of a strict partition are A304961.
Strict compositions of each part of a composition are A307068.
Compositions of each part of a strict composition are A336127.
Cf. A000012, A000244, A000302, A001906, A006951, A011782, A022811, A071919.
Cf. A072706, A078008, A112467, A182105, A316245, A336128, A336135.
Cf. A339006, A355382, A355384, A355387.

[n eq 0 select 1 else 3^(n-1): n in [0..30]]; // G. C. Greubel, Nov 20 2023

a:= n-> ceil(3^(n-1)):
seq(a(n), n=0..30);  # Alois P. Heinz, Jul 26 2020

CoefficientList[Series[(1 - 2 x)/(1 - 3 x), {x, 0, 50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)
Join[{1}, 3^(Range[0, 30])] (* G. C. Greubel, Nov 20 2023 *)

a(n)=max(1,3^(n-1)) \\ Charles R Greathouse IV, Jul 07 2011

Vec((1-2*x)/(1-3*x) + O(x^100)) \\  Altug Alkan, Oct 30 2015

[(3^n + 2*int(n==0))//3 for n in range(31)] # G. C. Greubel, Nov 20 2023

Binomial transform of A078008. - Paul Curtz, Aug 04 2008
From R. J. Mathar, Nov 11 2008: (Start)
G.f.: (1 - 2*x)/(1 - 3*x).
a(n) = A000244(n-1), n > 0. (End)
From Philippe Deléham, Nov 13 2008: (Start)
a(n) = Sum_{k=0..n} A112467(n,k)*2^k.
a(n) = Sum_{k=0..n} A071919(n,k)*2^k. (End)
Let A(x) be the g.f. Then B(x) = x*A(x) satisfies B(x/(1-x)) = x/(1 - 2*B(x)). - Vladimir Kruchinin, Dec 05 2011
G.f.: 1/(1 - (Sum_{k>=1} (x/(1 - x))^k)). - Joerg Arndt, Sep 30 2012
For n > 0, a(n) = 2*(Sum_{k=0..n-1} a(k)) - 1 = 3^(n-1). - J. Conrad, Oct 29 2015
G.f.: 1 + x/(1 + x)*(1 + 4*x/(1 + 4*x)*(1 + 7*x/(1 + 7*x)*(1 + 10*x/(1 + 10*x)*(1 + .... - Peter Bala, May 27 2017
Invert transform of A011782(n) = 2^(n-1). Second invert transform of A000012. - Gus Wiseman, Jul 19 2020
a(n) = ceiling(3^(n-1)). - Alois P. Heinz, Jul 26 2020
From Elmo R. Oliveira, Mar 31 2025: (Start)
E.g.f.: (2 + exp(3*x))/3.
a(n) = 3*a(n-1) for n > 1. (End)

Definition clarified by R. J. Mathar, Nov 11 2008

A046699 a(1) = a(2) = 1, a(n) = a(n - a(n-1)) + a(n-1 - a(n-2)) if n > 2.

Original entry on oeis.org

1, 1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 18, 19, 20, 20, 20, 21, 22, 22, 23, 24, 24, 24, 24, 25, 26, 26, 27, 28, 28, 28, 29, 30, 30, 31, 32, 32, 32, 32, 32, 32, 33, 34, 34, 35, 36, 36, 36, 37

Offset: 1

R. K. Guy

Ignoring first term, this is the meta-Fibonacci sequence for s=0. - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)

Except for the first term, n occurs A001511(n) times. - Franklin T. Adams-Watters, Oct 22 2006

Sequence was proposed by Reg Allenby.
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. See Eq. (2).
Michael Doob, The Canadian Mathematical Olympiad & L'Olympiade Mathématique du Canada 1969-1993, Canadian Mathematical Society & Société Mathématique du Canada, Problem 5, 1990, pp. 212-213, 1993.
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.

N. J. A. Sloane, Table of n, a(n) for n = 1..20000
Altug Alkan, On a Generalization of Hofstadter's Q-Sequence: A Family of Chaotic Generational Structures, Complexity (2018) Article ID 8517125.
Joerg Arndt, Matters Computational (The Fxtbook)
Stephen M. Buckley, Wiring switches to more light bulbs, arXiv:2410.02460 [math.CO], 2024. See pp. 3, 12, 22.
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. - _N. J. A. Sloane_, Apr 16 2014
M. Celaya and F. Ruskey, Morphic Words and Nested Recurrence Relations, arXiv preprint arXiv:1307.0153 [math.CO], 2013.
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences, J. Integer Seq., Vol. 12. [This is a later version than that in the GenMetaFib.html link]
C. Deugau and F. Ruskey, Complete k-ary Trees and Generalized Meta-Fibonacci Sequences
A. Erickson, A. Isgur, B. W. Jackson, F. Ruskey and S. M. Tanny, Nested recurrence relations with Conolly-like solutions, See Table 2.
Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv:1611.08244 [math.NT], 2016.
Nathan Fox, Trees, Fibonacci Numbers, and Nested Recurrences, Rutgers University Experimental Math Seminar, Mar 07, 2019.
Nathan Fox, Connecting Slow Solutions to Nested Recurrences with Linear Recurrent Sequences, arXiv:2203.09340 [math.CO], 2022.
The IMO Compendium, Problem 5, 22nd Canadian Mathematical Olympiad 1990.
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.
B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes
B. Jackson and F. Ruskey, Meta-Fibonacci Sequences, Binary Trees and Extremal Compact Codes, Electronic Journal of Combinatorics, 13 (2006), #R26, 13 pages.
Oliver Kullmann and Xishun Zhao, Parameters for minimal unsatisfiability: Smarandache primitive numbers and full clauses, arXiv preprint, arXiv:1505.02318 [cs.DM], 2015.
Thomas M. Lewis and Fabian Salinas, Optimal pebbling of complete binary trees and a meta-Fibonacci sequence, arXiv:2109.07328 [math.CO], 2021.
Ramin Naimi and Eric Sundberg, A Combinatorial Problem Solved by a Meta-Fibonacci Recurrence Relation, arXiv:1902.02929 [math.CO], 2019.
Index entries for Hofstadter-type sequences.
Index to sequences related to Olympiads.

Cf. A001511, A005185, A005187, A007843, A055938, A079559, A080578, A101925, A182105, A213714, A226222, A234016, A275363, A324473, A324475, A324477.

Callaghan et al. (2005)'s sequences T_{0,k}(n) for k=1 through 7 are A000012, A046699, A046702, A240835, A241154, A241155, A240830.

a046699 n = a046699_list !! (n-1)
a046699_list = 1 : 1 : zipWith (+) zs (tail zs) where
   zs = map a046699 $ zipWith (-) [2..] a046699_list
-- Reinhard Zumkeller, Jan 02 2012

[ n le 2 select 1 else Self(n - Self(n-1)) + Self(n-1 -Self(n-2)):n in [1..80]]; // Marius A. Burtea, Oct 17 2019

a := proc(n) option remember; if n <= 1 then return 1 end if; if n <= 2 then return 2 end if; return add(a(n - i + 1 - a(n - i)), i = 1 .. 2) end proc # Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)
a := proc(n) option remember; if n <= 2 then 1 else a(n - a(n-1)) + a(n-1 - a(n-2)); fi; end; # N. J. A. Sloane, Apr 16 2014

a[n_] := (k = 1; While[ !Divisible[(2*++k)!, 2^(n-1)]]; k); a[1] = a[2] = 1; Table[a[n], {n, 1, 72}] (* Jean-François Alcover, Oct 06 2011, after Benoit Cloitre *)
CoefficientList[ Series[1 + x/(1 - x)*Product[1 + x^(2^n - 1), {n, 6}], {x, 0, 80}], x] (* or *)
a[1] = a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[n - 1 - a[n - 2]]; Array[a, 80] (* Robert G. Wilson v, Sep 08 2014 *)

a[1]:1$
a[2]:1$
a[n]:=a[n-a[n-1]]+a[n-1-a[n-2]]$
makelist(a[n],n,2,60); /* Martin Ettl, Oct 29 2012 */

a(n)=if(n<0,1,s=1;while((2*s)!%2^(n-1)>0,s++);s) \\ Benoit Cloitre, Jan 19 2007

from sympy import factorial
def a(n):
    if n<3: return 1
    s=1
    while factorial(2*s)%(2**(n - 1))>0: s+=1
    return s
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 11 2017, after Benoit Cloitre

First differences seem to be A079559. - Vladeta Jovovic, Nov 30 2003. This is correct and not too hard to prove, giving the generating function x + x^2(1+x)(1+x^3)(1+x^7)(1+x^15).../(1-x). - Paul Boddington, Jul 30 2004
G.f.: x + x^2/(1-x) * Product_{n=1}^{infinity} (1 + x^(2^n-1)). - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)
For n>=1, a(n)=w(n-1) where w(n) is the least k such that 2^n divides (2k)!. - Benoit Cloitre, Jan 19 2007
Conjecture: a(n+1) = a(n) + A215530(a(n) + n) for all n > 0. - Velin Yanev, Oct 17 2019
From Bernard Schott, Dec 03 2021: (Start)
a(n) <= a(n+1) <=  a(n) +1.
For n > 1, if a(n) is odd, then a(n+1) = a(n) + 1.
a(2^n+1) = 2^(n-1) + 1 for n > 0.
Results coming from the 5th problem proposed during the 22nd Canadian Mathematical Olympiad in 1990 (link IMO Compendium and Doob reference). (End)

A082850 Let S(0) = {}, S(n) = {S(n-1), S(n-1), n}; sequence gives S(infinity).

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 6, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1, 1, 2, 3, 4, 5, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 1

Offset: 1

Benoit Cloitre, Apr 14 2003

Sequence counts up to successive values of A001511; i.e., apply the morphism k -> 1,2,...,k to A001511. If all 1's are removed from the sequence, the resulting sequence b has b(n) = a(n)+1. A101925 lists the positions of 1's in this sequence.

The geometric mean of this sequence approaches the Somos constant (A112302). - Jwalin Bhatt, Jan 30 2025

			S(1) = {1}, S(2) = {1,1,2}, S(3) = {1,1,2,1,1,2,3}, etc.

Alois P. Heinz, Table of n, a(n) for n = 1..65535

Cf. A082851 (partial sums).
Cf. A001511, A101925, A112302.
Cf. A215020.

Fold[Flatten[{#1, #1, #2}] &, {}, Range[5]] (* Birkas Gyorgy, Apr 13 2011 *)
Flatten[Table[Length@Last@Split@IntegerDigits[2 n, 2], {n, 20}] /. {n_ ->Range[n]}] (* Birkas Gyorgy, Apr 13 2011 *)

S = []; [S.extend(S + [n]) for n in range(1, 8)]
print(S) # Michael S. Branicky, Jul 02 2022

from itertools import count, islice
def A082850_gen(): # generator of terms
    S = []
    for n in count(1):
        yield from (m:=S+[n])
        S += m #
A082850_list = list(islice(A082850_gen(),20)) # Chai Wah Wu, Mar 06 2023

a(2^m - 1) = m.
If n = 2^m - 1 + k with 0 < k < 2^m, then a(n) = a(k). - Franklin T. Adams-Watters, Aug 16 2006
a(n) = log_2(A182105(n)) + 1. - Laurent Orseau, Jun 18 2019
a(n) = 1 + A215020(n). - Joerg Arndt, Mar 04 2025

A045412 a(1)=3; for n > 1, a(n) = a(n-1) + 1 if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.

Original entry on oeis.org

3, 6, 7, 10, 13, 14, 15, 18, 21, 22, 25, 28, 29, 30, 31, 34, 37, 38, 41, 44, 45, 46, 49, 52, 53, 56, 59, 60, 61, 62, 63, 66, 69, 70, 73, 76, 77, 78, 81, 84, 85, 88, 91, 92, 93, 94, 97, 100, 101, 104, 107, 108, 109, 112, 115, 116, 119, 122, 123, 124, 125, 126

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Apr 01 2003

nonn

It appears these are the indices of the terms in A182105 which are greater than 1. - Carl Joshua Quines, Apr 07 2017

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,3,1,3)-hiccup sequence. - Michael De Vlieger, Jul 30 2025

Indranil Ghosh, Table of n, a(n) for n = 1..10000
Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 15.
Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.
Geoffrey Powell, Symmetric powers, indecomposables and representation stability, arXiv:1809.08781 [math.AT], 2018.
Frank Ruskey and Chris Deugau, The Combinatorics of Certain k-ary Meta-Fibonacci Sequences, JIS 12 (2009) 09.4.3.

Cf. A080578.

l={3}; a=3; For[n=2, n<=100, If[MemberQ[l, n], a=a+1, a=a+3]; AppendTo[l, a]; n++]; l (* Indranil Ghosh, Apr 07 2017 *)

l=[3]
a=3
for n in range(2, 101):
    if n not in l: a+=3
    else: a+=1
    l.append(a)
print(l) # Indranil Ghosh, Apr 07 2017

A215026 Reluctant Fibonacci sequence.

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 5, 1, 1, 2, 1, 2, 3, 5, 8, 1, 1, 2, 1, 2, 3, 1, 1, 2, 3, 5, 8, 13, 1

Offset: 1

N. J. A. Sloane, Aug 03 2012

Donald E. Knuth, The Art of Computer Programming, Vol. 4, Pre-Fascicle 6A, Section 7.2.2.2, Problem 178, page 54.
Donald E. Knuth, Satisfiability, Fascicle 6, volume 4 of The Art of Computer Programming. Addison-Wesley, 2015, page 160, Problem 310; see solution on page 246.

Cf. A000045, A182105.

A339451 Gray-code-like sequence in which, at each step, the least significant bit that has never been toggled from the previous value, is toggled.

Original entry on oeis.org

0, 1, 0, 2, 3, 2, 0, 4, 5, 4, 6, 7, 6, 4, 0, 8, 9, 8, 10, 11, 10, 8, 12, 13, 12, 14, 15, 14, 12, 8, 0, 16, 17, 16, 18, 19, 18, 16, 20, 21, 20, 22, 23, 22, 20, 16, 24, 25, 24, 26, 27, 26, 24, 28, 29, 28, 30, 31, 30, 28, 24, 16, 0, 32, 33, 32, 34, 35, 34, 32, 36

Offset: 0

Allan C. Wechsler, Dec 05 2020

Conjectured connections: the position of the bit that is toggled to derive a(n) from a(n-1) is A215020(n); the sequence of absolute differences of this sequence is A182105; there is some underlying connection to the "skew binary" counting system.

			For n = 18, a(n-1) = 8. That is the second 8 in the sequence. We cannot toggle the 1-bit, because that was already used to derive a(16) = 9 from a(15) = 8, so instead we toggle the 2-bit, yielding a(n) = 10.

Alois P. Heinz, Table of n, a(n) for n = 0..65535

Cf. A182105, A215020.

a:= proc() local b, a; b:= proc() 1/2 end; a:= proc(n)
      option remember; local h; if n=0 then 0 else h:=
      a(n-1); b(h):= 2*b(h); Bits[Xor](h, b(h)) fi end
    end():
seq(a(n), n=0..127);  # Alois P. Heinz, Dec 05 2020

a[m_] := Module[{b, a}, b[] = 1/2; a[n] := a[n] =
     Module[{h}, If[n == 0 ,  0 ,  h = a[n - 1];
     b[h] = 2*b[h]; BitXor[h, b[h]]]]; a[m]];
Table[a[n], {n, 0, 127}] (* Jean-François Alcover, May 15 2022, after Alois P. Heinz *)

cp's OEIS Frontend

A215020 a(n) = log_2( A182105(n) ).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A133494 Diagonal of the array of iterated differences of A047848.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

PARI

SageMath

Formula

Extensions

A046699 a(1) = a(2) = 1, a(n) = a(n - a(n-1)) + a(n-1 - a(n-2)) if n > 2.

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

Maxima

PARI

Python

Formula

A082850 Let S(0) = {}, S(n) = {S(n-1), S(n-1), n}; sequence gives S(infinity).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

Python

Formula

A045412 a(1)=3; for n > 1, a(n) = a(n-1) + 1 if n is already in the sequence, a(n) = a(n-1) + 3 otherwise.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

A215026 Reluctant Fibonacci sequence.

Views

Author

Keywords

References

Crossrefs

A339451 Gray-code-like sequence in which, at each step, the least significant bit that has never been toggled from the previous value, is toggled.

Views

Author

Keywords

Comments

Examples

Links