

A256189


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 and gcd(a(n1), a(n)) = 1.


5



1, 2, 3, 4, 9, 10, 21, 5, 6, 25, 8, 15, 14, 27, 7, 12, 35, 22, 45, 11, 20, 33, 26, 51, 13, 17, 39, 34, 57, 16, 19, 18, 95, 28, 55, 38, 65, 24, 85, 46, 75, 23, 36, 115, 58, 69, 29, 30, 203, 32, 49, 50, 63, 44, 87, 62, 81, 31, 42, 155, 52, 93, 70, 99, 64, 77, 54
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The sequence is infinite because the term P*p is always a candidate for a(n), where p is a prime factor of a(n2) and P is a prime not dividing any of a(1),..., a(n1).
Moreover, this sequence conjecturally is a permutation of the positive integers: the proof iv for A098550 applies with essentially no changes, while vi still has a difficulty.


LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..1000
David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015.


MATHEMATICA

a[1]=1; a[2]=2; a[3]=3;
A256189 = {1, 2, 3};
a[n_] := a[n] = For[k=4, True, k++, If[FreeQ[A256189, k], If[PrimeQ[GCD[ a[n2], k]] && GCD[a[n1], k] == 1, AppendTo[A256189, k]; Return[k]]]];
A256189 = Array[a, 100] (* JeanFrançois Alcover, Aug 02 2018 *)


CROSSREFS

Cf. A098550, A256224, A256224.
Sequence in context: A295969 A174437 A127150 * A098548 A076963 A081871
Adjacent sequences: A256186 A256187 A256188 * A256190 A256191 A256192


KEYWORD

nonn


AUTHOR

Vladimir Shevelev, Mar 19 2015


EXTENSIONS

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


STATUS

approved



