A275068 Squarefree numbers in A022344.

1, 5, 11, 19, 29, 31, 41, 55, 59, 61, 71, 79, 89, 95, 101, 109, 131, 139, 145, 149, 151, 155, 179, 181, 191, 199, 205, 209, 211, 229, 239, 241, 251, 269, 271, 281, 295, 305, 311, 319, 331, 341, 349, 355, 359, 379, 389, 395, 401, 409, 419, 421, 431, 439, 445

Offset

0,2

Comments

The final digit of every number is 1, 5, or 9. As a set, A022344 consists of the numbers m*F^2, where m is in (1,5,11,19,...) and F is a Fibonacci number.

The restriction here to squarefree numbers excludes any of Wechsler's J determinants that derive from rows of the Wythoff array where all terms share a common factor, but there are also nonsquarefree numbers that are determinants of other rows: for example, 121 is the J determinant of row 45 (..., 3, 13, 16, 29, 45, 74, 119, 193, ...). Compare with A089270, which includes 121 and other such numbers. - Peter Munn, Aug 20 2025

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Example

A022344 = (1,5,4,9,16,11,19,11,20,31,19,31,45,29,... ), and deletion of 4,9,16,20, ... leaves (1,5,11,19,29,31,...).

Mathematica

g = GoldenRatio; a[n_] := Floor[(n + 1)*g]^2 - n*Floor[(n + 1)*g] - n^2;
u = Table[a[n], {n, 0, 200}]  (* A022344 *)
Union[Select[u, SquareFreeQ[#] &]]  (* A275068 *)

Crossrefs

Cf. A000045, A022344, A035513, A089270.

Sequence in context: A336015 A132087 A089270 * A038872 A141158 A239732

Adjacent sequences: A275065 A275066 A275067 * A275069 A275070 A275071

Keyword

nonn,easy

Author

Clark Kimberling, Jul 15 2016

Status

approved