A010695 -id:A010695 - cp's OEIS frontend

A010674 Period 2: repeat (0,3).

0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0

Offset: 0

N. J. A. Sloane

Also decimal expansion of 1/33 = .030303030...

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

Cf. A010680 (1/11), A010695 (2^(1 - (-1)^n) + 1).

&cat [[0,3]^^50]; // Bruno Berselli, Dec 29 2015

3Mod[Range[0, 99], 2] (* Alonso del Arte, Mar 25 2020 *)

makelist(if evenp(n) then 0 else 3, n, 0, 30); /* Martin Ettl, Nov 09 2012 */

a(n)=n%2*3 \\ Charles R Greathouse IV, Nov 20 2011

(0 to 99).map( % 2 * 3) // _Alonso del Arte, Mar 25 2020

a(n) = (3/2)*(1 - (-1)^n) = 3*(n mod 2). - Paolo P. Lava, Oct 20 2006
a(n) = A010698(n)/2 - 1. - Martin Ettl, Nov 11 2012
a(n) = 2^(1 - (-1)^n) - 1. - Bruno Berselli, Dec 29 2015
From Chai Wah Wu, Jun 04 2016: (Start)
a(n) = a(n-2) for n >= 2.
G.f.: 3*x/(1 - x^2). (End)
E.g.f.: 3*sinh(x). - Ilya Gutkovskiy, Jun 04 2016

More terms from Paolo P. Lava, Oct 20 2006

A010702 Period 2: repeat (3,4).

Original entry on oeis.org

3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3

Offset: 0

N. J. A. Sloane

Continued fraction expansion of A176102. - R. J. Mathar, Mar 08 2012

Also decimal expansion of 34/99. - Nicolas Bělohoubek, Nov 12 2021

Matthew House, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A047355 (partial sums), A176102.

Cf. A010695, A010696.

a010702 = (+ 3) . (`mod` 2)
a010702_list = cycle [3,4]  -- Reinhard Zumkeller, Jul 05 2012

[3 + (n mod 2) : n in [0..100]]; // Wesley Ivan Hurt, Jul 24 2014

&cat[[3,4]: n in [0..50]]; // Vincenzo Librandi, Aug 01 2015

A010702:=n->3+(n mod 2): seq(A010702(n), n=0..100); # Wesley Ivan Hurt, Jul 24 2014

3 + Mod[Range[0, 100], 2] (* Wesley Ivan Hurt, Jul 24 2014 *)
PadRight[{}, 100, {3, 4}] (* Vincenzo Librandi, Aug 01 2015 *)

a(n)=3+n%2 \\ Charles R Greathouse IV, Dec 21 2011

def A010702(n): return 3 + (n & 1) # Chai Wah Wu, May 25 2022

G.f.: (3+4*x)/(1-x^2). - Jaume Oliver Lafont, Mar 20 2009
a(n) = floor((n+1)*7/2) - floor((n)*7/2). - Hailey R. Olafson, Jul 23 2014
a(n) = 3 + (n mod 2) = 4 - ((n+1) mod 2). - Wesley Ivan Hurt, Jul 24 2014
From Nicolas Bělohoubek, Nov 12 2021: (Start)
a(n) = 12/a(n-1). See also A010696.
a(n) = 7 - a(n-1). See also A010695. (End)
a(n) = (7-(-1)^n)/2. - Aaron J Grech, Jul 28 2024

A010691 Period 2: repeat (1,10).

Original entry on oeis.org

1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10

Offset: 0

N. J. A. Sloane

Regular continued fraction of (5+sqrt 35)/10. - R. J. Mathar, Nov 21 2011

Sequence is an infinite palindrome in two ways (numbers and English names): ONE, TEN, ONE, TEN, ONE, TEN, ONE, ... . - Eric Angelini, Sep 16 2023

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A036117, A070341, A168429, A070367, A070392, A070404, A048271, A187466.

[10^n mod 11: n in [0..80]]; // Vincenzo Librandi, Aug 24 2011

g:=(1+10*z)/((1-z^2)): gser:=series(g, z=0, 66): seq((coeff(gser, z, n)), n=0..65); # Zerinvary Lajos, Feb 25 2009

PadRight[{},100,{1,10}] (* Harvey P. Dale, Aug 27 2013 *)

a(n) = -9/2*(-1)^n + 11/2.
G.f.: (1+10*z)/(1-z^2). - Zerinvary Lajos, Feb 25 2009
a(n) = 10^n mod 11. - M. F. Hasler, Mar 10 2011
From Nicolas Bělohoubek, Nov 11 2021: (Start)
a(n) = 10/a(n-1). See also A010695.
a(n) = 11 - a(n-1). See also A010712. (End)

A059855 Period of continued fraction for sqrt(n^2+4), n >= 1.

Original entry on oeis.org

1, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2

Offset: 1

Labos Elemer, Feb 27 2001

From Jianing Song, May 01 2021: (Start)
The old name was "Quotient cycle length of sqrt(n^2+4)."
Essentially the same as A010695 and A021400. (End)

			For even n, sqrt(n^2+4) = [n; n/2, 2*n], hence a(n) = 2.
For odd n > 1, sqrt(n^2+4) = [n; (n-1)/2, 1, 1, (n-1)/2, 2*n], hence a(n) = 5.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A003285, A010695, A021400.

Period of continued fraction for sqrt(n^2+k): A059853 (k=3), this sequence (k=4), A059854 (k=5).

with(numtheory): [seq(nops(cfrac(sqrt(k^2+4), 'periodic', 'quotients')[2]), k=1..100)];

a[n_] := Length @ ContinuedFraction[Sqrt[n^2 + 4]][[2]]; Array[a, 100] (* Amiram Eldar, May 13 2020 *)

a(n) = 2 for even n, a(n) = 5 for odd n > 1.

a(n) = A003285(n^2+4). - Jianing Song, May 01 2021

A176052 Decimal expansion of (5+sqrt(35))/5.

Original entry on oeis.org

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

Offset: 1

Klaus Brockhaus, Apr 07 2010

Continued fraction expansion of (5+sqrt(35))/5 is A010695.

			(5+sqrt(35))/5 = 2.18321595661992320851...

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

Cf. A010490 (decimal expansion of sqrt(35)), A010695 (repeat 2, 5).

A021400 Decimal expansion of 1/396.

Original entry on oeis.org

0, 0, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2, 5, 2

Offset: 0

N. J. A. Sloane

			0.0025252525252525252525252525252525252525252525252525...

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

A010695 shifted right.

First[RealDigits[1/396, 10, 100, -1]] (* or *)
PadRight[{0, 0}, 100, {2, 5}] (* Paolo Xausa, Aug 13 2025 *)

A176317 Decimal expansion of (5+sqrt(35))/2.

Original entry on oeis.org

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

Offset: 1

Klaus Brockhaus, Apr 15 2010

Continued fraction expansion of (5+sqrt(35))/2 is A010695.

			(5+sqrt(35))/2 = 5.45803989154980802128...

G. C. Greubel, Table of n, a(n) for n = 1..1000

Cf. A010490 (decimal expansion of sqrt(35)), A010695 (repeat 5, 2).

SetDefaultRealField(RealField(120)); (5 + Sqrt(35))/2; // G. C. Greubel, Nov 26 2019

evalf( (5 + sqrt(35))/2, 120); # G. C. Greubel, Nov 26 2019

RealDigits[(5+Sqrt[35])/2,10,120][[1]] (* Harvey P. Dale, Sep 21 2012 *)

default(realprecision, 120); (5 + sqrt(35))/2 \\ G. C. Greubel, Nov 26 2019

numerical_approx((5 + sqrt(35))/2, digits=120) # G. C. Greubel, Nov 26 2019

cp's OEIS Frontend

A010674 Period 2: repeat (0,3).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Maxima

PARI

Scala

Formula

Extensions

A010702 Period 2: repeat (3,4).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Magma

Maple

Mathematica

PARI

Python

Formula

A010691 Period 2: repeat (1,10).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula

A059855 Period of continued fraction for sqrt(n^2+4), n >= 1.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

A176052 Decimal expansion of (5+sqrt(35))/5.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A021400 Decimal expansion of 1/396.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

A176317 Decimal expansion of (5+sqrt(35))/2.

Views

Author

Keywords

Comments

Examples

Links