A372831 Decimal expansion of (16 + 5*sqrt(2))/15.

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

Offset

1,2

Links

Table of n, a(n) for n=1..86.

Index entries for algebraic numbers, degree 2.

Formula

Equals Sum_{k>=0} |cos(k*Pi/4)|/2^k.

Minimal polynomial: 225*x^2 - 480*x + 206. - Amiram Eldar, May 26 2026

Example

1.5380711874576983496005629080698993595232239584589826...

Mathematica

s = Sum[Abs[Cos[k  Pi/4]]/2^k, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]] (* A372831 *)
N[1/15  (16 + 5  Sqrt[2]), 100]
(* Alternative: *)
RealDigits[(16+5*Sqrt[2])/15, 10, 120][[1]] (* Harvey P. Dale, Nov 03 2024 *)

Prog

(PARI) (16+5*sqrt(2))/15 \\ Charles R Greathouse IV, Apr 30 2026

Crossrefs

Cf. A372778.

Sequence in context: A248257 A019663 A187488 * A087654 A086032 A018222

Adjacent sequences: A372828 A372829 A372830 * A372832 A372833 A372834

Keyword

nonn,cons,easy

Author

Clark Kimberling, Jun 07 2024

Status

approved