A055748 -id:A055748 - cp's OEIS frontend

A285578 a(1) = a(3) = a(4) = 2, a(2) = 1; a(n) = a(a(n-2)) + a(n-a(n-4)-2) for n > 4.

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

Offset: 1

Altug Alkan, Apr 22 2017

nonn

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Plot for first differences

Cf. A005185, A055748.

a[1] = a[3] = a[4] = 2; a[2] = 1; a[n_] := a[n] = a[a[n - 2]] + a[n - a[n - 4] - 2]; Array[a, 75] (* Michael De Vlieger, Apr 24 2017 *)

q=vector(10000); q[1]=q[3]=q[4]=2;q[2]=1; for(n=5, #q, q[n]=q[q[n-2]]+q[n-q[n-4]-2]); vector(10000, n, q[n])

A285582 a(1) = 1, a(2) = a(3) = a(4) = 2; a(n) = a(a(n-3)-1) + a(n-a(n-4)-1) for n > 4.

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5, 5, 7, 7, 7, 8, 8, 8, 8, 8, 8, 10, 10, 10, 13, 12, 13, 13, 12, 13, 13, 13, 13, 13, 13, 15, 15, 15, 20, 17, 20, 20, 17, 20, 18, 20, 20, 21, 21, 20, 21, 21, 21, 21, 21, 21, 21, 23, 23, 23, 28, 23, 28, 29, 23, 32, 28, 23, 31, 27, 28, 33, 33, 32

Offset: 1

Altug Alkan, Apr 22 2017

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Alternative scatterplot

Cf. A005185, A055748, A284523

a[1] = 1; a[2] = a[3] = a[4] = 2; a[n_] := a[n] = a[a[n - 3] - 1] + a[n - a[n - 4] - 1]; Array[a, 75] (* Michael De Vlieger, Apr 23 2017 *)

q=vector(10000); q[1]=1;q[2]=q[3]=q[4]=2; for(n=5, #q, q[n]=q[q[n-3]-1]+q[n-q[n-4]-1]); vector(10000, n, q[n])

A285588 a(1) = a(2) = 1; a(3) = a(4) = a(5) = 2; a(n) = a(a(n-3)-1) + a(n-a(n-5)-2) for n > 5.

Original entry on oeis.org

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

Offset: 1

Altug Alkan, Apr 22 2017

nonn

Altug Alkan, Table of n, a(n) for n = 1..10000
Altug Alkan, Alternative scatterplot

Cf. A005185, A055748.

a[1] = a[2] = 1; a[3] = a[4] = a[5] = 2; a[n_] := a[n] = a[a[n - 3] - 1] + a[n - a[n - 5] - 2]; Array[a, 80] (* Michael De Vlieger, Apr 23 2017 *)

q=vector(10000); q[1]=q[2]=1;q[3]=q[4]=q[5]=2; for(n=6, #q, q[n]=q[q[n-3]-1]+q[n-q[n-5]-2]); vector(10000, n, q[n])

A087834 a[n] =a[a[a[n-1]]] + a[n -1- a[n-2]].

Original entry on oeis.org

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

Offset: 1

Roger L. Bagula, Oct 07 2003

nonn

Triple recursion version of A055748.

Cf. A055748.

hg[n_Integer?Positive] := hg[n] =hg[hg[hg[n-1]]] + hg[n -1- hg[n-2]] hg[1] = hg[2] = 1 digits=200 a=Table[hg[n], {n, 1, digits}]

A330631 a(n+1) = a(n-a(n))+1 if a(n) > a(n-1), otherwise a(n+1) = 2*a(n); a(1) = a(2) = 1.

Original entry on oeis.org

1, 1, 2, 2, 4, 2, 4, 3, 6, 3, 6, 5, 10, 3, 6, 7, 7, 14, 3, 6, 4, 8, 4, 8, 8, 16, 4, 8, 7, 14, 8, 16, 8, 16, 15, 30, 3, 6, 17, 9, 18, 5, 10, 9, 18, 5, 10, 4, 8, 19, 9, 18, 17, 34, 7, 14, 6, 12, 6, 12, 5, 10, 19, 10, 20, 19, 38, 8, 16, 18, 19, 19, 38, 16, 32

Offset: 1

Rok Cestnik, Dec 21 2019

nonn

a(n) < n (with exception a(1) = 1). Proof: Suppose a(s) = s+x, x >= 0, is the first occurrence of a(n) >= n. From here we branch into two possibilities: Possibility #1: a(s-2) < a(s-1), from which it follows that a(s) = a(s-1-a(s-1))+1 and therefore a(s-1-a(s-1)) = s-1+x is an earlier example of a(n) >= n. Possibility #2: a(s-2) >= a(s-1) and the terms can be expressed as a(s-1) = (s+x)/2 and a(s-2) = (s+x)/2+y with y >= 0. From this it follows that a(s-2-((s+x)/2+y))+1 = (s+x)/2, which when simplified reveals that a((s+x)/2-2-x-y) = (s+x)/2-1 is an earlier example of a(n) >= n. Both possibilities lead to a contradiction of the first statement, therefore we conclude that there is no occurrence of a(n) >= n (with exception a(1) = 1).

Some numbers never seem to appear in the sequence; the smallest of these are 328, 329, 331, 332, 333, 445, 667, 668, 669, ...

			a(3) = 2*a(2) = 2 because a(2) <= a(1).
a(4) = a(3-a(3))+1 = 2 because a(3) > a(2).

See A281130 for a similar sequence.

Cf. A004001, A005229, A055748, A318281.

Nest[Append[#, If[Less @@ Take[#, -2], #[[Length@ # - #[[-1]] ]] + 1, 2 #[[-1]] ]] &, {1, 1}, 73] (* Michael De Vlieger, Dec 23 2019 *)

a = [1,1]
for n in range(1, 1000):
    if(a[n] > a[n-1]):
        a.append(a[n-a[n]]+1)
    else:
        a.append(2*a[n])

cp's OEIS Frontend

A285578 a(1) = a(3) = a(4) = 2, a(2) = 1; a(n) = a(a(n-2)) + a(n-a(n-4)-2) for n > 4.

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A285582 a(1) = 1, a(2) = a(3) = a(4) = 2; a(n) = a(a(n-3)-1) + a(n-a(n-4)-1) for n > 4.

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A285588 a(1) = a(2) = 1; a(3) = a(4) = a(5) = 2; a(n) = a(a(n-3)-1) + a(n-a(n-5)-2) for n > 5.

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A087834 a[n] =a[a[a[n-1]]] + a[n -1- a[n-2]].

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A330631 a(n+1) = a(n-a(n))+1 if a(n) > a(n-1), otherwise a(n+1) = 2*a(n); a(1) = a(2) = 1.

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