OFFSET
1,1
COMMENTS
Conjecture: This is a permutation of the nonsquares (A000037).
EXAMPLE
n a(n) Periodic part of continued fraction for square root of a(n)
-- ---- -----------------------------------------------------------
1 2 {2}
2 5 {4}
3 3 {1, 2}
4 10 {6}
5 6 {2, 4}
6 11 {3, 6}
7 7 {1, 1, 1, 4}
8 12 {2, 6}
9 8 {1, 4}
10 17 {8}
11 13 {1, 1, 1, 1, 6}
MATHEMATICA
pcf=Last@*ContinuedFraction@*Sqrt; a[1]=2; a[n_]:=a[n]=(k=2; While[MemberQ[Array[a, n-1], k]||IntegerQ@Sqrt@k||Intersection[pcf@a[n-1], pcf@k]!={}, k++]; k); Array[a, 100]
CROSSREFS
KEYWORD
nonn
AUTHOR
Giorgos Kalogeropoulos, Nov 23 2021
STATUS
approved