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

1,1

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.

Links

Table of n, a(n) for n=1..62.

Example

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.

Mathematica

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

Crossrefs

Cf. A003285, A002522, A121339.

Sequence in context: A182777 A214988 A028804 * A191894 A284955 A093480

Adjacent sequences: A345472 A345473 A345474 * A345476 A345477 A345478

Keyword

nonn

Author

Giorgos Kalogeropoulos, Sep 16 2021

Status

approved