

A256224


a(n) = n if n <= 3, otherwise a(n) is the smallest number not occurring earlier such that gcd(a(n2), a(n)) is a prime or a power of a prime (but not 1) and gcd(a(n1), a(n))=1.


3



1, 2, 3, 4, 9, 8, 15, 14, 5, 6, 25, 16, 35, 12, 7, 10, 21, 22, 27, 11, 18, 55, 26, 33, 13, 24, 65, 28, 39, 20, 51, 32, 17, 30, 119, 38, 49, 19, 42, 95, 34, 45, 44, 57, 40, 63, 46, 75, 23, 36, 115, 52, 69, 50, 81, 56, 87, 62, 29, 31, 58, 93, 64, 99, 68, 77, 48
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OFFSET

1,2


COMMENTS

The sequence is infinite.
Conjecture: This is a permutation of the natural numbers.


LINKS

Peter J. C. Moses and Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Peter J. C. Moses)
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015.


MATHEMATICA

a[n_] := a[n] = If[n <= 3, n, For[k = 1, True, k++, If[FreeQ[Array[a, n1], k], g = GCD[a[n2], k]; If[g>1 && PrimeNu[g] == 1 && GCD[a[n1], k] == 1, Return[k]]]]];
Array[a, 100] (* JeanFrançois Alcover, Aug 06 2018 *)


CROSSREFS

Cf. A098550, A256189.
Sequence in context: A329425 A247942 A098550 * A255509 A257862 A329449
Adjacent sequences: A256221 A256222 A256223 * A256225 A256226 A256227


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Mar 19 2015


EXTENSIONS

More terms from Peter J. C. Moses, Mar 24 2015


STATUS

approved



