OFFSET
1,2
COMMENTS
The sequences is conjectured to be a permutation of the positive integers. In the first 500000 terms there are 637 fixed points: 1, 2, 3, 6, 9, ..., 180611, 189383, 298097. As the terms slowly move away from the line a(n) = n as n increases it is likely no more exist.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Annotated log-log scatterplot of a(n), n - 1..2^14, showing records in red, local minima in blue, fixed points highlighted in amber, and primes in green.
Scott R. Shannon, Image of the first 500000 terms. The green line is y = n.
EXAMPLE
a(4) = 5 as (a(3)+a(2))*|a(3)-a(2)| = (3+2)*|3-2| = 5, and 5 is the smallest unused number that shares a factor with 5.
a(5) = 4 as (a(4)+a(3))*|a(4)-a(3)| = (5+3)*|5-3| = 16, and 4 is the smallest unused number that shares a factor with 16.
MATHEMATICA
nn = 74, c[_] = 0; Array[Set[{a[#], c[#]}, {#, #}] &, 2]; u = 3; Do[m = (#1 + #2) Abs[(#1 - #2)] & @@ {a[i - 1], a[i - 2]}; k = u; While[Nand[c[k] == 0, ! CoprimeQ[m, k]], k++]; Set[{a[i], c[k]}, {k, i}]; If[k == u, While[c[u] > 0, u++]], {i, Length[s] + 1, nn}]; Array[a, nn] (* Michael De Vlieger, Apr 17 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Scott R. Shannon, Apr 16 2022
STATUS
approved