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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). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

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 *)

PROG

(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))

CROSSREFS

Cf. A005132, A057167.

Sequence in context: A254155 A211342 A199401 * A159759 A243964 A197837

Adjacent sequences:  A261570 A261571 A261572 * A261574 A261575 A261576

KEYWORD

nonn

AUTHOR

Freddy Barrera, Aug 24 2015

STATUS

approved

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Last modified January 19 22:02 EST 2018. Contains 297938 sequences.