A040037 -id:A040037 - cp's OEIS frontend

A010498 Decimal expansion of square root of 44.

6, 6, 3, 3, 2, 4, 9, 5, 8, 0, 7, 1, 0, 7, 9, 9, 6, 9, 8, 2, 2, 9, 8, 6, 5, 4, 7, 3, 3, 4, 1, 3, 7, 3, 3, 6, 7, 8, 5, 4, 1, 7, 7, 0, 9, 1, 1, 7, 8, 7, 0, 7, 1, 9, 4, 1, 1, 7, 3, 6, 4, 2, 9, 2, 2, 3, 2, 9, 6, 9, 2, 8, 5, 2, 1, 8, 0, 8, 7, 6, 9, 3, 4, 1, 7, 6, 8, 6, 7, 9, 8, 2, 5, 6, 5, 8, 1, 3, 0

Offset: 1

N. J. A. Sloane

Continued fraction expansion is 6 followed by {1, 1, 1, 2, 1, 1, 1, 12} repeated. [Harry J. Smith, Jun 05 2009]

			6.633249580710799698229865473341373367854177091178707194117364292232969...

Harry J. Smith, Table of n, a(n) for n = 1..20000
Index entries for algebraic numbers, degree 2.

Cf. A040037 (continued fraction).

RealDigits[N[Sqrt[44],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2011 *)

{ default(realprecision, 20080); x=sqrt(44); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010498.txt", n, " ", d)); } \\ Harry J. Smith, Jun 05 2009

Equals 2*A010468. - R. J. Mathar, Jan 14 2021

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

Original entry on oeis.org

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

Frank Ellermann, Feb 23 2002

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

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

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.

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

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

Name clarified by Michel Marcus, Jun 22 2020

cp's OEIS Frontend

A010498 Decimal expansion of square root of 44.

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