A261573 A variation of Recamán's sequence A005132: Define a(0) = 0, and for n > 0, a(n) = a(n-1) - (n+2) if positive and not already in the sequence, otherwise a(n) = a(n-1) + (n+2).

0, 3, 7, 2, 8, 1, 9, 18, 28, 17, 5, 18, 4, 19, 35, 52, 34, 15, 35, 14, 36, 13, 37, 12, 38, 11, 39, 10, 40, 71, 103, 70, 104, 69, 33, 70, 32, 71, 31, 72, 30, 73, 29, 74, 120, 167, 119, 168, 118, 67, 119, 66, 120, 65, 121, 64, 6, 65, 125, 186, 124, 61, 125, 60, 126, 59, 127, 58, 128, 57

Offset: 0

Author

Freddy Barrera, Aug 24 2015

Keywords

• nonn

Comments

As in Recamán's sequence, terms are repeated, the first being 18 = a(7) = a(11).

More generally, for k >= 0, a_k(0) = 0, and for n > 0, a_k(n) = a_k(n-1) - (n+k) if positive and not already in the sequence, otherwise a_k(n) = a_k(n-1) + (n+k).

For k = 0, this is Recamán's sequence A005132.

Links

• Freddy Barrera, Table of n, a(n) for n = 0..10000
• Freddy Barrera, Line plot of the first 1000 terms.
• Freddy Barrera, Scatter plot of the first 1000 terms.
• Freddy Barrera, Line plot of the first 1000 terms when k = 0, 1, 2, ..., 9
• Freddy Barrera, Scatter plot of the first 1000 terms when k = 0, 1, 2, ..., 9

Crossrefs

Cf. A005132, A057167.

Programs

Mathematica

f[s_List] := Block[{a = s[[-1]], len = Length@ s}, Append[s, If[a > len + 1 && ! MemberQ[s, a - len - 2], a - len - 2, a + len + 2]]]; Nest[f, {0}, 70] (* Robert G. Wilson v, Sep 08 2015 *)

Python

def sequence(n, k):
    """For n > 0 and k >= 0, generates the first n terms of the sequence"""
    A, a = {0}, 0
    yield a
    for n in range(1, n + 1):
        a = a - (n + k)
        if a > 0 and a not in A:
            A.add(a)
            yield a
        else:
            a = a + 2 * (n + k)
            A.add(a)
            yield a
# List of the first 1000 terms of the sequence with k = 2.
list(sequence(1000, 2))