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

Author

Alonso del Arte, Dec 25 2024

Keywords

• nonn
• cons
• easy

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.

Examples

			72.883468633154391...
		

Links

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

Crossrefs

Cf. A010534, the square root of 83.

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(5312); // Vincenzo Librandi, Jan 02 2025

Mathematica

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

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