A343069 Decimal expansion of 2*(1+5*sqrt(2))/7.

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

Offset

1,1

Comments

Dissect the unit square into 7 regions with equal areas from a given midpoint on the squares edge. This sequence gives the decimal expansion of the perimeter of the triangular region with unit height.

Links

Table of n, a(n) for n=1..93.

Index entries for algebraic numbers, degree 2.

Formula

Equals 2*(1 + k*sqrt(1/k^2 + 1))/k, where k = 7.

Minimal polynomial: 7*x^2 - 4*x - 28. - Amiram Eldar, May 30 2026

Example

2.3060193748187072125738410...

Mathematica

RealDigits[2 (1 + 5 Sqrt[2])/7, 10, 200][[1]] // Flatten

Prog

(PARI) 2*(1+5*sqrt(2))/7 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Similar sequences into k regions: A344520 (k=3), A344554 (k=5), A344568 (k=9), A344569 (k=17).

Sequence in context: A321296 A190902 A115562 * A127468 A173720 A173717

Adjacent sequences: A343066 A343067 A343068 * A343070 A343071 A343072

Keyword

nonn,cons

Author

Wesley Ivan Hurt, May 23 2021

Status

approved