A174930 -id:A174930 - cp's OEIS frontend

A174927 Periodic sequence: Repeat 1, 64.

1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64, 1, 64

Offset: 0

Klaus Brockhaus, Apr 02 2010

Interleaving of A000012 and 2*A010871.
Also continued fraction expansion of (4+sqrt(17))/8.
First differences of A174928.

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

Cf. A000012 (all 1's sequence), A010871 (all 32's sequence), A010689 (repeat 1, 8), A174930 (decimal expansion of (4+sqrt(17))/8), A174928.

&cat[ [1, 64]: n in [0..41] ];
[ (65-63*(-1)^n)/2: n in [0..83] ];

PadRight[{},100,{1,64}] (* Harvey P. Dale, Jun 16 2013 *)

a(n) = (65-63*(-1)^n)/2.
a(n) = a(n-2) for n > 1; a(0) = 0, a(1) = 64.
a(n) = -a(n-1)+65 for n > 0; a(0) = 1.
a(n) = ((n+1) mod 2)+64*(n mod 2).
G.f.: (1+64*x)/((1-x)*(1+x)).

A358945 Decimal expansion of the positive root of 4*x^2 + x - 1.

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang, Jan 20 2023

The negative root is -(A189038 - 1) = -0.6403882032... .

c^n = A052923(-n) + A006131(-(n+1))*phi17, for n >= 0, with phi17 = A222132 = (1 + sqrt(17))/2, A052923(-n) = -(-2*i)^(-n)*S(-(n+2), i/2) = (i/2)^n*S(n, i/2), with i = sqrt(-1), and A006131(-(n+1)) = A052923(-n+1)/4 = -(i/2)^(n+1)*S(n-1, i/2), with the S-Chebyshev polynomials (see A049310), and S(-n, x) = -S(n-2, x), for n >= 1. - Wolfdieter Lang, Jan 04 2024

			c = 0.39038820320220756872767623199675962814339990317170255429982919663...

Index entries for sequences related to Chebyshev polynomials.

Cf. A006131, A010473, A049310, A052923, A174930, A189038, A222132.

RealDigits[(Sqrt[17] - 1)/8, 10, 120][[1]] (* Amiram Eldar, Jan 20 2023 *)
RealDigits[Root[4x^2+x-1,2],10,120][[1]] (* Harvey P. Dale, Jan 15 2024 *)

c = (-1 + sqrt(17))/8 = A189038 - 5/4 = A174930 - 5/8.

c = 1/phi17 = (-1 + phi17)/4, with phi17 = A222132. - Wolfdieter Lang, Jan 05 2024

cp's OEIS Frontend

A174927 Periodic sequence: Repeat 1, 64.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula