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.

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

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

Michael De Vlieger, Table of n, a(n) for n = 0..16383

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 * A377305 A284549 A200779

Adjacent sequences: A321338 A321339 A321340 * A321342 A321343 A321344

Keyword

nonn,easy

Author

David Nacin, Nov 05 2018

Status

approved