A344176 - OEIS

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A344176

Alternating parity Yellowstone permutation: a(n) = n if n <= 3, 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 the terms in the sequence alternate parity.

1, 2, 3, 4, 9, 8, 15, 14, 5, 6, 25, 12, 35, 16, 7, 10, 21, 20, 27, 22, 39, 28, 13, 18, 65, 24, 55, 26, 11, 30, 77, 32, 33, 34, 45, 38, 51, 40, 17, 36, 85, 42, 95, 44, 19, 46, 57, 50, 63, 52, 49, 48, 91, 54, 119, 58, 105, 62, 69, 56, 23, 60, 161, 64, 115, 66

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Coincides with the Yellowstone permutation A098550 up to the term a(21).

The primes that appear at the same indices in both sequences are 2,3,5,7 and 13. It seems these are the only ones since due to the alternating parity condition, the primes in a(n) appear at larger indices than in A098550 (however, there are composites that appear at the same indices in both sequences, for example a(47)=57 and a(52)=48).

Even with the alternating parity condition, the primes seem to appear in their natural order as in the Yellowstone permutation (conjecture 8 in A098550), except for 11 and 13, which appear in reverse order.

Unlike the Yellowstone permutation, there seems to be an infinite number of fixed points.

LINKS

Table of n, a(n) for n=1..66.

Rémy Sigrist, PARI program for A344176

Index entries for sequences that are permutations of the natural numbers

MATHEMATICA

Block[{a = Range[3], k}, Do[k = 4; While[Nand[FreeQ[a, k], GCD[a[[-2]], k] > 1, GCD[a[[-1]], k] == 1, UnsameQ @@ Mod[{a[[-1]], k}, 2]], k++]; AppendTo[a, k], {i, 63}]; a] (* Michael De Vlieger, May 14 2021 *)

PROG

(PARI) See Links section.

CROSSREFS

Cf. A098550.

Sequence in context: A374612 A098550 A335585 * A256224 A340783 A255509

Adjacent sequences: A344173 A344174 A344175 * A344177 A344178 A344179

KEYWORD

nonn

AUTHOR

Enrique Navarrete, May 10 2021

STATUS

approved