A108575 Numbers k such that the continued fraction for sqrt(k) is multiplicative.

3, 7, 8, 13, 14, 15, 22, 23, 24, 32, 33, 34, 35, 44, 47, 48, 58, 59, 60, 62, 63, 74, 75, 78, 79, 80, 95, 96, 98, 99, 114, 119, 120, 135, 136, 138, 140, 141, 142, 143, 160, 162, 164, 167, 168, 185, 187, 189, 192, 194, 195, 215, 219, 220, 222, 223, 224, 248, 252, 254

Offset

1,1

Comments

m^2 - m < a(n) < m^2 for some m.

Links

Table of n, a(n) for n=1..60.

Example

The continued fraction for sqrt(7) is c = (2, 1, 1, 1, 4, 1, 1, 1, 4, ...) = A010121. If we index starting at 0, so that c(0) = 2, c is multiplicative (the value at c(0) is immaterial). Hence 7 is in the sequence.

Crossrefs

Cf. A010121, A109054 (with squares included).

Sequence in context: A153030 A031425 A063657 * A153219 A264720 A215034

Adjacent sequences: A108572 A108573 A108574 * A108576 A108577 A108578

Keyword

nonn

Author

David W. Wilson, Jun 10 2005

Status

approved