A345709 A variation on the Yellowstone permutation: a(n) = n if n <= 3, a(4) = 5; otherwise the smallest number not occurring earlier having at least one common factor with a(n-2), but none with a(n-1), with the condition that two odd terms alternate with one even term.

1, 2, 3, 5, 6, 25, 9, 10, 21, 55, 12, 11, 15, 22, 27, 77, 18, 7, 33, 14, 39, 35, 24, 49, 45, 28, 51, 91, 30, 13, 57, 26, 19, 65, 38, 75, 133, 20, 63, 85, 36, 17, 69, 34, 23, 119, 46, 105, 253, 40, 99, 95, 42, 115, 81, 50, 87, 125, 48, 145, 93, 58, 31, 29, 62, 203, 155, 56, 135, 161, 54

Offset

1,2

Comments

Unlike the Yellowstone permutation (A098550) and the alternating parity Yellowstone permutation (A344176), the primes do not appear in their natural order. Indeed, after the initial conditions 2, 3 and 5, the next primes to appear are 11, 7, 13, 19, 17, 23, 31, 29.

Not a permutation of the positive integers since no larger powers of 2 appear as terms of the sequence.

Links

Table of n, a(n) for n=1..71.

Sean A. Irvine, Java program (github)

Mathematica

Array[(a@#=#)&, 3]; a[4]=5; a[n_]:=a[n]=(If[And@@OddQ[{a[n-1], a[n-2]}], k=2, k=1]; While[MemberQ[Array[a, n-1], k]||GCD[a[n-2], k]<2||GCD[a[n-1], k]>1, k=k+2]; k); Array[a, 100] (* Giorgos Kalogeropoulos, Jul 23 2021 *)

Crossrefs

Cf. A098550, A344176.

Sequence in context: A238335 A131599 A263650 * A076384 A261579 A270517

Adjacent sequences: A345706 A345707 A345708 * A345710 A345711 A345712

Keyword

nonn

Author

Enrique Navarrete, Jun 24 2021

Status

approved