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A272636
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a(0)=0, a(1)=1; thereafter a(n) = squarefree part of a(n-1)+a(n-2).
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5
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0, 1, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7, 1, 2, 3, 5, 2, 7
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OFFSET
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0,4
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COMMENTS
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Periodic with period {1,2,3,5,2,7}.
James Propp, in a posting to the Math Fun list, asks if every sequence of positive numbers satisfying the same recurrence will eventually merge with this sequence (as A272638 does). The answer is no, Fred W. Helenius found infinitely many counterexamples, including A272637. See A272639 for other counterexamples which start 1,x.
Other counterexamples found by Helenius include [n, 2n, 3n, 5n, 2n, 7n] (period 6) where n is any squarefree positive integer coprime to 210 = 2*3*5*7.
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LINKS
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Table of n, a(n) for n=0..115.
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MATHEMATICA
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{0, 1}~Join~LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 2, 3, 5, 2, 7}, 120] (* Jean-François Alcover, Nov 16 2019 *)
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PROG
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(Python)
from sympy.ntheory.factor_ import core
l=[0, 1]
for n in range(2, 101):
l.append(core(l[n - 1] + l[n - 2]))
print(l) # Indranil Ghosh, Jun 03 2017
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CROSSREFS
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Cf. A007913 (squarefree part of n), A000045, A272637, A272638, A272639.
See A165911 for a similar sequence.
See also A214674, A214892-A214898.
Sequence in context: A053723 A201652 A359609 * A066949 A073481 A178094
Adjacent sequences: A272633 A272634 A272635 * A272637 A272638 A272639
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, May 05 2016
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STATUS
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approved
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