A308419 Stopping time for Recamán-like iteration of each n: a(0) = n, a(k) = a(k-1) - k if positive and not already in the sequence, a(k) = a(k-1) + k if not already in the sequence, otherwise stop.

24, 24, 13, 21, 3, 3, 3, 15, 6, 6, 6, 15, 12, 9, 9, 9, 16, 20, 15, 12, 12, 12, 8, 10, 12, 20, 15, 15, 15, 10, 15, 24, 22, 26, 18, 18, 18, 11, 13, 18, 29, 28, 27, 21, 21, 21, 15, 13, 19, 17, 25, 31, 23, 24, 24, 24, 16, 18, 20, 21

Offset

0,1

Comments

a(0) is the index of the first repeated value in Recamán's sequence (A005132).

a(n) appears to grow like sqrt(2n).

Links

Table of n, a(n) for n=0..59.

Example

For n = 8, the Recamán-like sequence generated is 8, 7, 5, 2, 6, 1; the sequence halts after a(8) = 6 terms since 1 - 6 = -5 is negative and 1 + 6 = 7 is already in the sequence.

Prog

(Python 3)
def seqr(n):
    sequence = [n]
    i = 1
    while True:
        if n - i > 0 and n - i not in sequence:
            n -= i
            sequence.append(n)
        elif n + i not in sequence:
            n += i
            sequence.append(n)
        else:
            break
        i += 1
    return len(sequence)
print([seqr(n) for n in range(1000)])

Crossrefs

Iteration rule nearly identical to A005132.

A334219 is essentially the same sequence.

Sequence in context: A022980 A023466 A278656 * A010863 A362116 A217140

Adjacent sequences: A308416 A308417 A308418 * A308420 A308421 A308422

Keyword

nonn

Author

Kevin J. Gomez, May 25 2019

Status

approved