A020819 -id:A020819 - cp's OEIS frontend

A010515 Decimal expansion of square root of 62.

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

Offset: 1

N. J. A. Sloane

Sqrt(62) = 787400 * Sum_{n>=0} (A001790(n)/2^A005187(floor(n/2)) * 10^(-6n-5)) where A001790(n) are numerators in expansion of 1/sqrt(1-x) and the denominators in expansion of 1/sqrt(1-x) are 2^A005187(n). 786400 = 62*12700, see A020819 (expansion of 1/sqrt(62)). - Gerald McGarvey, Jan 01 2005

Continued fraction expansion is 7 followed by {1, 6, 1, 14} repeated. - Harry J. Smith, Jun 07 2009

			7.874007874011811019685034448812007863681086122020853794598842550313760...

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

Cf. A001790, A005187, A020819.

Cf. A010146 Continued fraction.

RealDigits[N[62^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)

{ default(realprecision, 20080); x=sqrt(62); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010515.txt", n, " ", d)); } \\ Harry J. Smith, Jun 07 2009

Final digits of sequence corrected using the b-file. - N. J. A. Sloane, Aug 30 2009

A041109 Denominators of continued fraction convergents to sqrt(62).

Original entry on oeis.org

1, 1, 7, 8, 119, 127, 881, 1008, 14993, 16001, 110999, 127000, 1888999, 2015999, 13984993, 16000992, 237998881, 253999873, 1761998119, 2015997992, 29985970007, 32001967999, 221997778001, 253999746000, 3777994222001, 4031993968001, 27969958030007

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0,0,0,126,0,0,0,-1).

Cf. A041108, A010146, A020819, A010515.

I:=[1, 1, 7, 8, 119, 127, 881, 1008]; [n le 8 select I[n] else 126*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Denominator[Convergents[Sqrt[62], 30]] (* Vincenzo Librandi, Dec 11 2013 *)
LinearRecurrence[{0,0,0,126,0,0,0,-1},{1,1,7,8,119,127,881,1008},30] (* Harvey P. Dale, Oct 26 2016 *)

G.f.: -(x^2-x-1)*(x^4+8*x^2+1) / (x^8-126*x^4+1). - Colin Barker, Nov 12 2013

a(n) = 126*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 11 2013

More terms from Colin Barker, Nov 12 2013

cp's OEIS Frontend

A010515 Decimal expansion of square root of 62.

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