A040461 -id:A040461 - cp's OEIS frontend

A176400 Decimal expansion of sqrt(483).

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

Offset: 2

Klaus Brockhaus, Apr 17 2010

Continued fraction expansion of sqrt(483) is A040461.

			sqrt(483) = 21.97726097583591056720...

Daniel Starodubtsev, Table of n, a(n) for n = 2..10000

Cf. A010477 (decimal expansion of sqrt(21)), A010479 (decimal expansion of sqrt(23)), A176399 (decimal expansion of (21+sqrt(483))/7), A040461.

RealDigits[Sqrt[483],10,120][[1]] (* Harvey P. Dale, Oct 09 2015 *)

A041923 Denominators of continued fraction convergents to sqrt(483).

Original entry on oeis.org

1, 1, 43, 44, 1891, 1935, 83161, 85096, 3657193, 3742289, 160833331, 164575620, 7073009371, 7237584991, 311051578993, 318289163984, 13679196466321, 13997485630305, 601573592939131, 615571078569436, 26455558892855443, 27071129971424879

Offset: 0

N. J. A. Sloane

The following remarks assume an offset of 1. This is the sequence of Lehmer numbers U_n(sqrt(R),Q) for the parameters R = 42 and Q = -1; it is a strong divisibility sequence, that is, gcd(a(n),a(m)) = a(gcd(n,m)) for all positive integers n and m. Consequently, this is a divisibility sequence: if n divides m then a(n) divides a(m). - Peter Bala, May 27 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Eric W. Weisstein, MathWorld: Lehmer Number
Index entries for linear recurrences with constant coefficients, signature (0,44,0,-1).

Cf. A041922, A176400, A040461, A002530.

I:=[1,1,43,44]; [n le 4 select I[n] else 44*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 27 2013

Denominator[Convergents[Sqrt[483], 30]] (* Vincenzo Librandi, Dec 27 2013 *)

G.f.: -(x^2 -x -1) / (x^4 -44*x^2 +1). - Colin Barker, Nov 27 2013
a(n) = 44*a(n-2) - a(n-4) for n > 3. - Vincenzo Librandi, Dec 27 2013
From Peter Bala, May 27 2014: (Start)
The following remarks assume an offset of 1.
Let alpha = ( sqrt(42) + sqrt(46) )/2 and beta = ( sqrt(42) - sqrt(46) )/2 be the roots of the equation x^2 - sqrt(42)*x - 1 = 0. Then a(n) = (alpha^n - beta^n)/(alpha - beta) for n odd, while a(n) = (alpha^n - beta^n)/(alpha^2 - beta^2) for n even.
a(n) = Product_{k = 1..floor((n-1)/2)} ( 42 + 4*cos^2(k*Pi/n) ).
Recurrence equations: a(0) = 0, a(1) = 1 and for n >= 1, a(2*n) = a(2*n - 1) + a(2*n - 2) and a(2*n + 1) = 42*a(2*n) + a(2*n - 1). (End)

More terms from Colin Barker, Nov 27 2013

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A176400 Decimal expansion of sqrt(483).

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