A040035 -id:A040035 - cp's OEIS frontend

A010496 Decimal expansion of square root of 42.

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

Offset: 1

N. J. A. Sloane

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

			6.480740698407860230965967436087996657705204307058346549711354397809617....

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

Cf. A040035 (continued fraction).

RealDigits[N[Sqrt[42],200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 24 2011 *)

default(realprecision, 20080); x=sqrt(42); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010496.txt", n, " ", d));  \\ Harry J. Smith, Jun 05 2009

A041071 Denominators of continued fraction convergents to sqrt(42).

Original entry on oeis.org

1, 2, 25, 52, 649, 1350, 16849, 35048, 437425, 909898, 11356201, 23622300, 294823801, 613269902, 7654062625, 15921395152, 198710804449, 413343004050, 5158826853049, 10730996710148, 133930787374825, 278592571459798, 3477041644892401, 7232675861244600

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 (0,26,0,-1).

Cf. A010496, A040035, A041070 (numerators).

I:=[1, 2, 25, 52]; [n le 4 select I[n] else 26*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 10 2013

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[42],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 22 2011 *)
Denominator[Convergents[Sqrt[42], 30]] (* Vincenzo Librandi, Dec 10 2013 *)
LinearRecurrence[{0,26,0,-1},{1,2,25,52},30] (* Harvey P. Dale, Oct 17 2019 *)

G.f.: -(x^2-2*x-1) / (x^4-26*x^2+1). - Colin Barker, Nov 12 2013

a(n) = 26*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 10 2013

More terms from Colin Barker, Nov 12 2013

cp's OEIS Frontend

A010496 Decimal expansion of square root of 42.

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