A063882 -id:A063882 - cp's OEIS frontend

A136036 a(n) = A063882(n+1) - A063882(n).

0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0

Offset: 1

Reinhard Zumkeller, Dec 11 2007

nonn

0 <= a(n) <= 1; 1 <= a(n)+a(n+1)+a(n+2) <= 2 for n>5.

B. Balamohan, A. Kuznetsov and S. Tanny, On the behavior of a variant of Hofstadter's Q-sequence, JIS, Vol. 10 (2007), #07.7.1

Cf. A063882.

A132173 Maternal generation number of A063882(n).

Original entry on oeis.org

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

Offset: 1

N. J. A. Sloane, Nov 07 2007

nonn

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.
Index entries for Hofstadter-type sequences

A278055 Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 5.

Original entry on oeis.org

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

Offset: 1

Nathan Fox, Nov 10 2016

nonn

This sequence is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

A number k appears twice in this sequence if and only if for some i, k is congruent to A057198(i) mod 3^i and k > A057198(i).

Nathan Fox, Table of n, a(n) for n = 1..10000
Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv preprint arXiv:1611.08244 [math.NT], 2016.

Cf. A005185, A057198, A063882, A267501, A274058.

a[n_] := a[n] = a[n - a[n -1]] + a[n - a[n -2]] + a[n - a[n -3]]; a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 4; a[5] = 5; Array[a, 71] (* Robert G. Wilson v, Dec 02 2016 *)

A=Vecsmall([]);
a(n)=if(n<7, return(n)); if(#ACharles R Greathouse IV, Nov 19 2016

a(n) ~ 2n/3.

A063892 a(1) = a(2) = a(3) = 1, a(n) = a(n-a(n-2))+a(n-a(n-3)) for n>3.

Original entry on oeis.org

1, 1, 1, 2, 4, 6, 5, 3, 3, 9, 6, 4, 7, 12, 9, 5, 7, 10, 16, 16, 10, 12, 12, 16, 14, 21, 13, 17, 8, 14, 24, 26, 19, 12, 8, 23, 22, 23, 12, 17, 18, 28, 35, 26, 16, 22, 34, 47, 22, 6, 10, 36, 69, 36

Offset: 1

Henry Bottomley, Aug 29 2001

Undefined for n>54 since a(53)=69>=55.

			a(7) = a(7-a(5))+a(7-a(4)) = a(7-4)+a(7-2) = a(3)+a(5) = 1+4 = 5.

Cf. A005185, A046700, A063882, A226222.

See A064714 for a variant which does not die.

#Q(r,s) with initial values 1,1,1,..., from N. J. A. Sloane, Apr 15 2014
r:=2; s:=3;
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..54)];

A087777 a(1) = ... = a(4) = 1; a(n) = a(n - a(n-2)) + a(n - a(n-4)).

Original entry on oeis.org

1, 1, 1, 1, 2, 4, 6, 7, 7, 5, 3, 8, 9, 11, 12, 9, 9, 13, 11, 9, 13, 16, 13, 19, 16, 11, 14, 16, 21, 22, 14, 14, 19, 17, 22, 27, 25, 16, 20, 28, 22, 22, 26, 25, 24, 32, 26, 22, 29, 29, 32, 35, 32, 27, 26, 34, 30, 33, 40, 25, 27, 46, 40, 33, 32, 28, 36, 50, 44, 31, 36, 38, 46, 53, 41, 29, 41

Offset: 1

Roger L. Bagula, Oct 05 2003

nonn

This is the sequence Q(2,4) in the Hofstadter-Huber classification.

It is not known if this sequence is defined for all positive n. Balamohan et al. comment that it shows "inscrutably wild behavior".

N. J. A. Sloane, Table of n, a(n) for n = 1..10000
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.
Nathan Fox, A Slow Relative of Hofstadter's Q-Sequence, arXiv:1611.08244 [math.NT], 2016.
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 100000 terms
Index entries for Hofstadter-type sequences

Cf. A005185 (Q(1,2)), A063882 (Q(1,4)), A046700.

[n le 4 select 1 else Self(n-Self(n-2))+Self(n-Self(n-4)): n in [1..80]]; // Vincenzo Librandi, Sep 10 2016

a := proc(n) option remember; if n<=4 then 1 else if n > a(n-2) and n > a(n-4) then RETURN(a(n-a(n-2))+a(n-a(n-4))); else ERROR(" died at n= ", n); fi; fi; end;

a[n_] := a[n] = If[n <= 4, 1, a[n - a[n - 2]] + a[n - a[n - 4]]];
Array[a, 80] (* Jean-François Alcover, Nov 24 2017 *)

Edited by N. J. A. Sloane, Nov 06 2007

A285757 a(n) = a(n - a(n - 2)) + a(n - a(n - 8)), with a(i) = i for 1 <= i <= 9.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 10, 10, 11, 12, 12, 12, 13, 14, 15, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 22, 22, 22, 22, 22, 23, 24, 24, 24, 25, 26, 27, 28, 28, 28, 29, 30, 30, 30, 31, 32, 33, 34, 34, 34, 34, 34, 35, 36, 36, 36, 37, 38, 39

Offset: 1

Nathan Fox, Apr 25 2017

nonn

The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

This sequence can be obtained from A063882 using a construction of Isgur et al.

Nathan Fox, Table of n, a(n) for n = 1..10000
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

Cf. A005185, A063882, A285758, A285759, A285760, A285761, A285762.

A285757:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 3: elif n = 4 then 4: elif n = 5 then 5: elif n = 6 then 6: elif n = 7 then 7: elif n = 8 then 8: elif n = 9 then 9: else A285757(n-A285757(n-2)) + A285757(n-A285757(n-8)): fi: end:

A285758 A slow relative of Hofstadter's Q sequence.

Original entry on oeis.org

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

Offset: 1

Nathan Fox, Apr 25 2017

nonn

a(n) is the solution to the recurrence relation a(n) = a(n-a(n-2)) + a(n-a(n-8)), with the initial conditions: a(1) = 1, a(i) = 2 for 2 <= i <= 8, and a(9) = 3.
The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.
This sequence can be obtained from A063882 using a construction of Isgur et al.

Nathan Fox, Table of n, a(n) for n = 1..10000
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

Cf. A005185, A063882, A285757, A285759, A285760, A285761, A285762.

A285758:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 2: elif n = 4 then 2: elif n = 5 then 2: elif n = 6 then 2: elif n = 7 then 2: elif n = 8 then 2: elif n = 9 then 3: else A285758(n-A285758(n-2)) + A285758(n-A285758(n-8)): fi: end:

A285759 a(n) = a(n - 1 - a(n - 1)) + a(n - 1 - a(n - 4)), with a(1) = 1, a(2) = 1, a(3) = 1, a(4) = 2.

Original entry on oeis.org

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

Offset: 1

Nathan Fox, Apr 25 2017

nonn

The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

Nathan Fox, Table of n, a(n) for n = 1..10000
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

Cf. A005185, A063882, A285757, A285758, A285760, A285761, A285762.

A285759:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 1: elif n = 4 then 2: else A285759(n-1-A285759(n-1)) + A285759(n-1-A285759(n-4)): fi: end:

A285760 a(n) = a(n - 2 - a(n - 1)) + a(n - 2 - a(n - 4)), with a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 2.

Original entry on oeis.org

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

Offset: 1

Nathan Fox, Apr 25 2017

nonn

The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

Nathan Fox, Table of n, a(n) for n = 1..10000
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

Cf. A005185, A063882, A285757, A285758, A285759, A285761, A285762.

A285760:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 2: elif n = 4 then 2: else A285760(n-2-A285760(n-1)) + A285760(n-2-A285760(n-4)): fi: end:

A285761 A slow relative of Hofstadter's Q sequence.

Original entry on oeis.org

1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 14, 15, 15, 15, 16, 16, 16, 17, 17, 18, 19, 19, 19, 20, 20, 20, 21, 21, 22, 23, 23, 23, 24, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 29

Offset: 1

Nathan Fox, Apr 25 2017

nonn

a(n) is the solution to the recurrence relation a(n) = a(n-4-a(n-1)) + a(n-4-a(n-4)), with the initial conditions: a(1) = 1, a(2) = 2, a(3) = a(4) = a(5) = 3, a(6) = a(7) = a(8) = 4, a(9) = a(10) = 5.

The sequence a(n) is monotonic, with successive terms increasing by 0 or 1. So the sequence hits every positive integer.

Nathan Fox, Table of n, a(n) for n = 1..10000
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

Cf. A005185, A063882, A285757, A285758, A285759, A285760, A285762.

A285761:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 2: elif n = 3 then 3: elif n = 4 then 3: elif n = 5 then 3: elif n = 6 then 4: elif n = 7 then 4: elif n = 8 then 4: elif n = 9 then 5: elif n = 10 then 5: else A285761(n-4-A285761(n-1)) + A285761(n-4-A285761(n-4)): fi: end:

cp's OEIS Frontend

A136036 a(n) = A063882(n+1) - A063882(n).

Views

Author

Keywords

Comments

Links

Crossrefs

A132173 Maternal generation number of A063882(n).

Views

Author

Keywords

Links

A278055 Relative of Hofstadter Q-sequence: a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4, a(5) = 5; a(n) = a(n-a(n-1)) + a(n-a(n-2)) + a(n-a(n-3)) for n > 5.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A063892 a(1) = a(2) = a(3) = 1, a(n) = a(n-a(n-2))+a(n-a(n-3)) for n>3.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

A087777 a(1) = ... = a(4) = 1; a(n) = a(n - a(n-2)) + a(n - a(n-4)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Extensions

A285757 a(n) = a(n - a(n - 2)) + a(n - a(n - 8)), with a(i) = i for 1 <= i <= 9.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

A285758 A slow relative of Hofstadter's Q sequence.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

A285759 a(n) = a(n - 1 - a(n - 1)) + a(n - 1 - a(n - 4)), with a(1) = 1, a(2) = 1, a(3) = 1, a(4) = 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

A285760 a(n) = a(n - 2 - a(n - 1)) + a(n - 2 - a(n - 4)), with a(1) = 1, a(2) = 1, a(3) = 2, a(4) = 2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs