A176057 -id:A176057 - cp's OEIS frontend

A010700 Period 2: repeat (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, 10, 2, 10

Offset: 0

N. J. A. Sloane

Continued fraction expansion of A176057. - R. J. Mathar, Mar 08 2012

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

Cf. A010679: 3^(1-(-1)^n) - 1.

Equals 2 + A010679 = 2 + 8*A000035.

&cat [[2,10]^^35]; // Bruno Berselli, Dec 29 2015

A010700 := n -> 2 + irem(n,2)*8; # M. F. Hasler, Feb 27 2020

PadRight[{}, 100, {2, 10}] (* M. F. Hasler, Feb 27 2020 *)

a(n)=2+n%2*8 \\ Charles R Greathouse IV, Dec 21 2011

apply( {A010700(n)=2+bittest(n,0)<<3}, [0..99]) \\ M. F. Hasler, Feb 27 2020

a(n) = -4*(-1)^n + 6. Paolo P. Lava, Oct 20 2006
G.f. (2+10*x)/((1-x)*(1+x)). - R. J. Mathar, Nov 21 2011
a(n) = 3^(1-(-1)^n) + 1. - Bruno Berselli, Dec 29 2015
a(n) = 2 + 8*(n mod 2) = 2 + 8*A000035(n). - M. F. Hasler, Feb 27 2020

A245294 Decimal expansion of the square root of 6/5.

Original entry on oeis.org

1, 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

Jean-François Alcover, Jul 17 2014

Decimal expansion of the Landau-Kolmogorov constant C(4,2) for derivatives in the case L_infinity(infinity, infinity).
See A245198.
Apart from the first digit the same as A176057. - R. J. Mathar, Jul 21 2014

			1.095445115010332226913939565601604267905489389995966508453788899464986554...

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 3.3 Landau-Kolmogorov constants, p. 213.

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000
Eric Weisstein's MathWorld, Landau-Kolmogorov Constants.
Eric Weisstein's MathWorld, Favard Constants.

Cf. A050970, A050971, A244091, A245198.

a[n_] := (4/Pi)*Sum[((-1)^j/(2*j+1))^(n+1), {j, 0, Infinity}]; c[n_, k_] := a[n-k]*a[n]^(-1+k/n); RealDigits[c[4, 2], 10, 105] // First
RealDigits[Sqrt[6/5], 10, 100][[1]] (* Amiram Eldar, Jul 19 2022 *)

sqrt(6/5) \\ Charles R Greathouse IV, Aug 26 2017

C(n,k) = a(n-k)*a(n)^(-1+k/n), where a(n) = (4/Pi)*sum_{j=0..infinity}((-1)^j/(2j+1))^(n+1) or a(n) = 4*Pi^n*f(n+1), f(n) being the n-th Favard constant A050970(n)/A050971(n).
C(4,2) = sqrt(6/5).
Equals Sum_{k>=0} binomial(2*k,k)/24^k. - Amiram Eldar, Jul 19 2022

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A010700 Period 2: repeat (2,10).

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A245294 Decimal expansion of the square root of 6/5.

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