A067280 Number of terms in continued fraction for sqrt(n), excl. 2nd and higher periods.

1, 2, 3, 1, 2, 3, 5, 3, 1, 2, 3, 3, 6, 5, 3, 1, 2, 3, 7, 3, 7, 7, 5, 3, 1, 2, 3, 5, 6, 3, 9, 5, 5, 5, 3, 1, 2, 3, 3, 3, 4, 3, 11, 9, 7, 13, 5, 3, 1, 2, 3, 7, 6, 7, 5, 3, 7, 8, 7, 5, 12, 5, 3, 1, 2, 3, 11, 3, 9, 7, 9, 3, 8, 6, 5, 13, 7, 5, 5, 3, 1, 2, 3, 3, 6, 11, 3, 7, 6, 3, 9, 9, 11, 17, 5, 5, 12, 5

Offset

1,2

References

H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th edition, 1999, table 1.

Links

Table of n, a(n) for n=1..98.

Formula

a(n) = A003285(n) + 1. - Andrey Zabolotskiy, Jun 23 2020

Example

a(2)=2: [1,(2)+ ]; a(3)=3: [1,(1,2)+ ]; a(4)=1: [2]; a(5)=2: [2,(4)+ ].

Prog

(Python)
from sympy import continued_fraction_periodic
def A067280(n): return len((a := continued_fraction_periodic(0, 1, n))[:1]+(a[1] if a[1:] else [])) # Chai Wah Wu, Jun 14 2022

Crossrefs

Related sequences: 2 : A040000, ..., 44: A040037, 48: A040041, ..., 51: A040043, 56: A040048, 60: A040052, 63: A040055, ..., 66: A040057. 68: A040059, 72: A040063, 80: A040071.

Related sequences: 45: A010135, ..., 47: A010137, 52: A010138, ..., 55: A010141, 57: A010142, ..., 59: A010144. 61: A010145, 62: A010146. 67: A010147, 69: A010148, ..., 71: A010150.

Cf. A003285.

Sequence in context: A350604 A011448 A174981 * A167157 A238837 A309940

Adjacent sequences: A067277 A067278 A067279 * A067281 A067282 A067283

Keyword

nonn,easy

Author

Frank Ellermann, Feb 23 2002

Extensions

Name clarified by Michel Marcus, Jun 22 2020

Status

approved