A379556 Decimal expansion of the square root of 5312.

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

Offset

2,1

Comments

Continued fraction begins 72 then 1, 7, 1, 1, 2, 1, 1, 2, 1, 35, 1, 2, 1, 1, 2, 1, 1, 7, 1, 144, repeated.

The number sqrt(5312) is an algebraic integer in Z[sqrt(83)] as sqrt(5312) = 8 sqrt(83). Z[sqrt(83)] is a unique factorization domain, and 5312 factorizes as (9 - sqrt(83))^6 (9 + sqrt(83))^6 sqrt(83)^2.

Links

Table of n, a(n) for n=2..129.

The Late Show with Stephen Colbert, "How Does TV Work?" - Stephen Colbert Answers Real Questions From Real Kids. Relevant part starts at 3:10.

Example

72.883468633154391...

Mathematica

RealDigits[Sqrt[5312], 10, 100][[1]]

Prog

(Scala) import java.math.{BigDecimal, MathContext, RoundingMode}
val num = BigDecimal.valueOf(5312)
val mc = new MathContext(128, RoundingMode.HALF_EVEN)
val root = num.sqrt(mc)
root.toString.replace(".", "").toCharArray.toList
(Magma) SetDefaultRealField(RealField(100)); Sqrt(5312); // Vincenzo Librandi, Jan 02 2025

Crossrefs

Cf. A010534, the square root of 83.

Sequence in context: A363538 A048836 A198673 * A086236 A244354 A125126

Adjacent sequences: A379553 A379554 A379555 * A379557 A379558 A379559

Keyword

nonn,cons,easy

Author

Alonso del Arte, Dec 25 2024.

Status

approved