login
A345475
Nonsquares k whose continued fraction for the square root of k has a periodic part that is a nondecreasing sequence.
0
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved