A345475 Nonsquares k whose continued fraction for the square root of k has a periodic part that is a nondecreasing sequence.

2, 3, 5, 6, 7, 8, 10, 11, 12, 13, 15, 17, 18, 20, 24, 26, 27, 30, 32, 35, 37, 38, 39, 40, 41, 42, 48, 50, 51, 55, 56, 58, 63, 65, 66, 68, 72, 74, 75, 80, 82, 83, 84, 87, 90, 99, 101, 102, 104, 105, 110, 120, 122, 123, 130, 132, 135, 136, 143, 145, 146, 147

Offset: 1

Author

Giorgos Kalogeropoulos, Sep 16 2021

Keywords

• nonn

Comments

All k = m^2 + 1 (A002522) belong in the sequence because the periodic part of the continued fraction of sqrt(k) has a single element.

Examples

			a(5)=7 because the periodic part of the continued fraction of sqrt(7) is (1,1,1,4) which is a nondecreasing sequence.
19 is not a term because the periodic part of the continued fraction of sqrt(19) is (2, 1, 3, 1, 2, 8) which is not a nondecreasing sequence.
		

Crossrefs

Cf. A003285, A002522, A121339.

Programs

Mathematica

Select[Range@147,!IntegerQ@Sqrt@#&&OrderedQ@Last@ContinuedFraction[Sqrt@#]&]