

A308419


Stopping time for Recamánlike iteration of each n: a(0) = n, a(k) = a(k1)  k if positive and not already in the sequence, a(k) = a(k1) + k if not already in the sequence, otherwise stop.


1



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
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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 Recamánlike 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 A217140 A235249
Adjacent sequences: A308416 A308417 A308418 * A308420 A308421 A308422


KEYWORD

nonn


AUTHOR

Kevin J. Gomez, May 25 2019


STATUS

approved



