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

Author

Clark Kimberling, Jul 15 2016

Keywords

• nonn
• easy

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

Examples

			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,...).
		

Links

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

Crossrefs

Cf. A000045, A022344, A035513, A089270.

Programs

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 *)