A223141 Decimal expansion of (sqrt(29) - 1)/2.

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

Offset

1,1

Comments

Decimal expansion of sqrt(7 - sqrt(7 - sqrt(7 - sqrt(7 - ... )))).

Sequence with a(1) = 3 is decimal expansion of sqrt(7 + sqrt(7 + sqrt(7 + sqrt(7 + ... )))) - A223140.

Links

Table of n, a(n) for n=1..102.

Index entries for algebraic numbers, degree 2.

Formula

Closed form: (sqrt(29) - 1)/2 = A098318-3 = 10*A085551+2 = A223140-1.

sqrt(7 - sqrt(7 - sqrt(7 - sqrt(7 - ... )))) + 1 = sqrt(7 + sqrt(7 + sqrt(7 + sqrt(7 + ... )))). See A223140.

Minimal polynomial: x^2 + x - 7. - Amiram Eldar, Jun 08 2026

Example

2.1925824035672520156253552457701...

Mathematica

RealDigits[(Sqrt[29] - 1)/2, 10, 130][[1]]

Prog

(PARI) (sqrt(29)-1)/2 \\ Charles R Greathouse IV, May 19 2026

Crossrefs

Cf. A098318, A085551, A223140.

Sequence in context: A095890 A292827 A243999 * A021460 A090884 A369919

Adjacent sequences: A223138 A223139 A223140 * A223142 A223143 A223144

Keyword

nonn,cons,changed

Author

Jaroslav Krizek, Apr 02 2013

Status

approved