A120703 Decimal expansion of limiting difference of n - Sum_{k=0..n} cos(Pi/2^k).

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

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Lim_{n->oo} (n - Sum_{k=0..n} cos(Pi/2^k)).

Equals -1 + 2*Sum_{k=0..oo} (sin(2*Pi/2^k))^2. - G. C. Greubel, Aug 25 2023

Example

2.3946498021251655592210031427120730939115471925612304123083093845833338...

Mathematica

N[n - Sum[Cos[Pi/2^k], {k, 0, n}] /. n -> 300, 80] RealDigits[%, 10]
RealDigits[-1 +2*Sum[Sin[2*Pi/2^k]^2, {k, 0, 1000}], 10, 155][[1]] (* G. C. Greubel, Aug 25 2023 *)

Prog

(Magma) R:= RealField(151); -1 + 2*(&+[ Sin(Pi(R)/2^(k-1))^2 : k in [0..1000]]) // G. C. Greubel, Aug 25 2023
(SageMath) numerical_approx( -1 + 2*sum( sin(pi/2^(k-1))^2 for k in range(1001)), digits=150) # G. C. Greubel, Aug 25 2023

Crossrefs

Sequence in context: A160388 A358057 A026195 * A222120 A242812 A363679

Adjacent sequences: A120700 A120701 A120702 * A120704 A120705 A120706

Keyword

cons,nonn

Author

Joseph Biberstine (jrbibers(AT)indiana.edu), Jun 28 2006

Extensions

More digits from Jon E. Schoenfield, Mar 21 2021

Status

approved