A046699 -id:A046699 - cp's OEIS frontend

A316626 a(1)=a(2)=a(3)=1; a(n) = a(n-2a(n-1))+a(n-1-2a(n-2)) for n > 3.

1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20

Offset: 1

Nathan Fox and Altug Alkan, Jul 08 2018

nonn

This sequence increases slowly, and each term repeats at least three times.

If k is not a power of 2, then k appears in this sequence the same number of times as it appears in A081832. Otherwise, it appears exactly one additional time.

Nathan Fox, Table of n, a(n) for n = 1..10000
A. Erickson, A. Isgur, B. W. Jackson, F. Ruskey and S. M. Tanny, Nested recurrence relations with Conolly-like solutions, See Conjecture 5.1.

Cf. A005185, A046699, A081832.

a:=[1,1,1];; for n in [4..80] do a[n]:=a[n-2*a[n-1]]+a[n-1-2*a[n-2]]; od; a; # Muniru A Asiru, Jul 09 2018

[n le 3 select 1  else Self(n-2*Self(n-1))+Self(n-1-2*Self(n-2)): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018

A316626:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 1: elif n = 2 then 1: elif n = 3 then 1: else A316626(n-2*A316626(n-1)) + A316626(n-1-2*A316626(n-2)): fi: end:

a(n+1)-a(n)=1 or 0.

a(n)/n -> C=1/4.

A316627 a(1)=2, a(2)=3; a(n) = a(n+1-a(n-1))+a(n-a(n-2)) for n > 2.

Original entry on oeis.org

2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 13, 14, 14, 15, 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, 33, 34, 34, 35, 36, 36, 36, 37, 38, 38, 39, 40, 40, 40, 40, 41, 42, 42

Offset: 1

Nathan Fox, Jul 08 2018

nonn

This sequence increases slowly.
If k is not a power of 2, k occurs A001511(k) times. Otherwise, k occurs A001511(k)-1 times.
This is the meta-Fibonacci sequence for s=-1.

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).

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

Cf. A001511, A005185, A006949, A046699.

a:=[2,3];; for n in [3..75] do a[n]:=a[n+1-a[n-1]]+a[n-a[n-2]]; od; a; # Muniru A Asiru, Jul 09 2018

I:=[2,3]; [n le 2 select I[n] else Self(n+1-Self(n-1))+Self(n-Self(n-2)): n in [1..100]]; // Vincenzo Librandi, Jul 09 2018

A316627:=proc(n) option remember: if n <= 0 then 0: elif n = 1 then 2: elif n = 2 then 3: else A316627(n + 1-A316627(n-1)) + A316627(n-A316627(n-2)): fi: end:

a(n+1)-a(n)=1 or 0.

a(n)/n -> C=1/2.

A340619 n appears A006519(n) times.

Original entry on oeis.org

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

Offset: 1

Rémy Sigrist, Jan 13 2021

This sequence has similarities with the Cantor staircase function.
This sequence can be seen as an irregular table where the n-th row contains A006519(n) times the value n.
For any k > 1, the set of points { (n, a(n)), n = 1..A006520(2^k-1) } is symmetric; for example, for k = 3, we have the following configuration:
      a(n)
       ^
       |           *
       |         **
       |        *
       |    ****
       |   *
       | **
       |*
       +-------------> n

			The first rows, alongside A006519(n), are:
    n | n-th row               | A006519(n)
   ---+------------------------+-----------
    1 | 1                      |          1
    2 | 2, 2                   |          2
    3 | 3                      |          1
    4 | 4, 4, 4, 4             |          4
    5 | 5                      |          1
    6 | 6, 6                   |          2
    7 | 7                      |          1
    8 | 8, 8, 8, 8, 8, 8, 8, 8 |          8
    9 | 9                      |          1
   10 | 10, 10                 |          2

Rémy Sigrist, Table of n, a(n) for n = 1..11264
Wikipedia, Cantor function

See A061392 and A340500 for similar sequences.

Cf. A006519, A006520, A046699.

A340619[n_] := Array[n &, Table[BitAnd[BitNot[i - 1], i], {i, 1, n}][[n]]];
Table[A340619[n], {n, 1, 26}] // Flatten (* Robert P. P. McKone, Jan 19 2021 *)

concat(apply(v -> vector(2^valuation(v,2), k, v), [1..26]))

a(n) = my(ret=0); forstep(k=logint(n,2),0,-1, if(n > k<<(k-1), ret+=1<Kevin Ryde, Jan 18 2021

a(A006520(n)) = n.
a(A006520(n)+1) = n+1.
a(n) + a(A006520(2^k-1) + 1 - n) = 2^k for any k > 0 and n = 1..A006520(2^k-1).
a(n) = 2^k + (a(r) if r>0), where k such that k*2^(k-1) < n <= (k+1)*2^k and r = n - (k+2)*2^(k-1). - Kevin Ryde, Jan 18 2021

A339310 a(n) = a(n-1-a(n-1)) + a(n-a(n-2)) for n>2; starting with a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 2, 3, 3, 3, 5, 4, 6, 5, 6, 8, 8, 6, 9, 8, 8, 11, 11, 10, 10, 14, 12, 11, 16, 15, 12, 17, 14, 17, 16, 18, 14, 19, 19, 16, 21, 22, 19, 21, 25, 18, 22, 25, 23, 24, 25, 25, 23, 31, 28, 22, 33, 28, 29, 32, 28, 29, 30, 30, 33, 35, 29, 33, 32, 28, 41, 36, 35

Offset: 1

Pablo Hueso Merino, Dec 02 2020

nonn

{a(n)} is the Pinn F 1,0(n) sequence (see link section).

			a(3)=2 because a(3) = a(3-1-a(3-1))+a(3-a(3-2)) = a(2-1)+a(3-1) = 1+1 = 2.

K. Pinn, A Chaotic Cousin Of Conway's Recursive Sequence, arXiv:cond-mat/9808031 [cond-mat.stat-mech], 1998.

Cf. A005185, A070867, A046699.

a[1] = a[2] = 1; a[n_] := a[n] = a[n - 1 - a[n - 1]] + a[n - a[n - 2]]; Table[ a[n], {n, 1, 40}]

lista(nn) = {my(va = vector(nn)); va[1] = 1; va[2] = 1; for (n=3, nn, va[n]=va[n-1-va[n-1]]+va[n-va[n-2]];); va;} \\ Michel Marcus, Dec 07 2020

a=[1,1]
for n in range(100):
    i1=len(a)-1-a[len(a)-1]
    i2=len(a)-a[len(a)-2]
    if i1>=0 and i2>=0 :
        a.append(a[i1]+a[i2])
    else :
        print("Sequence dies. Contains ", n+2, " terms.")
        break
print(a)

cp's OEIS Frontend

A316626 a(1)=a(2)=a(3)=1; a(n) = a(n-2*a(n-1))+a(n-1-2*a(n-2)) for n > 3.

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A316627 a(1)=2, a(2)=3; a(n) = a(n+1-a(n-1))+a(n-a(n-2)) for n > 2.

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A340619 n appears A006519(n) times.

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A339310 a(n) = a(n-1-a(n-1)) + a(n-a(n-2)) for n>2; starting with a(1) = a(2) = 1.

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A316626 a(1)=a(2)=a(3)=1; a(n) = a(n-2a(n-1))+a(n-1-2a(n-2)) for n > 3.