A010700 -id:A010700 - cp's OEIS frontend

A040024 Continued fraction for sqrt(30).

5, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2

Offset: 0

N. J. A. Sloane

			5.4772255750516611345696978... = 5 + 1/(2 + 1/(10 + 1/(2 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009

James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Harry J. Smith, Table of n, a(n) for n = 0..20000
G. Xiao, Contfrac
Index entries for continued fractions for constants
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010485 (decimal expansion), A010700.

Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):

ContinuedFraction[Sqrt[30],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

{ allocatemem(932245000); default(realprecision, 28000); x=contfrac(sqrt(30)); for (n=0, 20000, write("b040024.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

G.f.: (5 + 2*x + 5*x^2)/(1 - x^2). - Stefano Spezia, Jul 26 2025

A176057 Decimal expansion of (5+sqrt(30))/5.

Original entry on oeis.org

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

Offset: 1

Klaus Brockhaus, Apr 07 2010

Continued fraction expansion of (5+sqrt(30))/5 is A010700.

			(5+sqrt(30))/5 = 2.09544511501033222691...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010485 (decimal expansion of sqrt(30)), A010700 (repeat 2, 10).

A010679 Period 2: repeat (0,8).

Original entry on oeis.org

0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0, 8, 0

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A010700: 3^(1-(-1)^n) + 1.

&cat [[0,8]^^40]; // Bruno Berselli, Dec 29 2015

PadRight[{},120,{0,8}] (* Harvey P. Dale, Dec 21 2015 *)

a(n)=n%2*8 \\ Charles R Greathouse IV, Jul 26 2016

a(n) = 4*(1-(-1)^n) = 8*(n mod 2). - Paolo P. Lava, Oct 20 2006
G.f.: 8*x/((1-x)*(1+x)). - R. J. Mathar, Nov 21 2011
a(n) = 3^(1-(-1)^n) - 1. - Bruno Berselli, Dec 29 2015

A137797 a(n) = 2( (n+1) mod 5 ) - 2( (n+1) mod 2 ).

Original entry on oeis.org

0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6, 0, 0, 4, 4, 8, -2, 2, 2, 6, 6

Offset: 0

William A. Tedeschi, Feb 10 2008

The sequence is periodic with period 10. - Colin Barker, Dec 16 2014

			a(2) = 2*((2+1) mod 5) - 2*((2+1) mod 2) = 2*(3 mod 5) - 2*(3 mod 2) = 4.

Index entries for linear recurrences with constant coefficients, signature (-1,0,0,0,1,1).

Suggested by A010700. Used in A137798.

LinearRecurrence[{-1,0,0,0,1,1},{0,4,4,8,-2,2},100] (* Harvey P. Dale, Jun 08 2015 *)

concat(0, Vec(-2*x*(3*x^3+6*x^2+4*x+2)/((x-1)*(x+1)*(x^4+x^3+x^2+x+1)) + O(x^100))) \\ Colin Barker, Dec 16 2014

a(n) = -a(n-1)+a(n-5)+a(n-6) for n>5. - Colin Barker, Dec 16 2014

G.f.: -2*x*(3*x^3+6*x^2+4*x+2) / ((x-1)*(x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Dec 16 2014

A176529 Decimal expansion of 5+sqrt(30).

Original entry on oeis.org

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

Offset: 2

Klaus Brockhaus, Apr 24 2010

Continued fraction expansion of 5+sqrt(30) is A010700 preceded by 10.

a(n) = A010485(n-2) for n > 3.

			5+sqrt(30) = 10.47722557505166113456...

Cf. A010485 (decimal expansion of sqrt(30)), A010700 (repeat 2, 10).

RealDigits[5+Sqrt[30],10,120][[1]]  (* Harvey P. Dale, Mar 31 2011 *)

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A040024 Continued fraction for sqrt(30).

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A176057 Decimal expansion of (5+sqrt(30))/5.

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A010679 Period 2: repeat (0,8).

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A137797 a(n) = 2*( (n+1) mod 5 ) - 2*( (n+1) mod 2 ).

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A176529 Decimal expansion of 5+sqrt(30).

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A137797 a(n) = 2( (n+1) mod 5 ) - 2( (n+1) mod 2 ).