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A321341 An unbounded sequence which is 1 infinitely often, with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms. 2
1, 1, 1, 2, 2, 1, 3, 3, 4, 1, 4, 5, 5, 1, 6, 6, 7, 1, 7, 8, 8, 1, 9, 9, 10, 1, 10, 11, 11, 1, 12, 12, 13, 1, 13, 14, 14, 1, 15, 15, 16, 1, 16, 17, 17, 1, 18, 18, 19, 1, 19, 20, 20, 1, 21, 21, 22, 1, 22, 23, 23, 1, 24, 24, 25, 1, 25, 26, 26, 1, 27, 27, 28, 1, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
This sequence was constructed to show that there are many sequences, besides those merging with multiples of the Padovan sequence A000931, with the property that for any four consecutive terms the maximum term is the sum of the two minimum terms. This refutes a conjecture that was formerly in that entry.
LINKS
David Nacin, Van der Laan Sequences and a Conjecture on Padovan Numbers, J. Int. Seq., Vol. 26 (2023), Article 23.1.2.
MATHEMATICA
{3#+1, 1, 3#+1, 3#+2, 3#+2, 1, 3#+3, 3#+3}& /@ Range[0, 9] // Flatten (* Jean-François Alcover, Nov 24 2018, from Python *)
PROG
(Python)
l=list()
for a in range(10):
l+=[3*a+1, 1, 3*a+1, 3*a+2, 3*a+2, 1, 3*a+3, 3*a+3]
(PARI) a(n)={my(t=n\8*3); [t+1, 1, t+1, t+2, t+2, 1, t+3, t+3][n%8 + 1]} \\ Andrew Howroyd, Nov 19 2018
CROSSREFS
Exhibits a property shared with multiples of A000931.
Sequence in context: A109524 A191521 A245370 * A284549 A200779 A286558
KEYWORD
nonn,easy
AUTHOR
David Nacin, Nov 05 2018
STATUS
approved

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Last modified May 26 13:56 EDT 2024. Contains 372826 sequences. (Running on oeis4.)