cp's OEIS Frontend

A379556 Decimal expansion of the square root of 5312.

%I A379556 #19 Jul 09 2025 05:07:48
%S A379556 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,
%T A379556 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,
%U A379556 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
%N A379556 Decimal expansion of the square root of 5312.
%C A379556 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.
%C A379556 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.
%H A379556 The Late Show with Stephen Colbert, <a href="https://youtu.be/xdpqh43rbbk?si=IzaHHGCG4ybguZX2&amp;t=190">"How Does TV Work?" - Stephen Colbert Answers Real Questions From Real Kids</a>. Relevant part starts at 3:10.
%e A379556 72.883468633154391...
%t A379556 RealDigits[Sqrt[5312], 10, 100][[1]]
%o A379556 (Scala) import java.math.{BigDecimal, MathContext, RoundingMode}
%o A379556 val num = BigDecimal.valueOf(5312)
%o A379556 val mc = new MathContext(128, RoundingMode.HALF_EVEN)
%o A379556 val root = num.sqrt(mc)
%o A379556 root.toString.replace(".", "").toCharArray.toList
%o A379556 (Magma) SetDefaultRealField(RealField(100)); Sqrt(5312); // _Vincenzo Librandi_, Jan 02 2025
%Y A379556 Cf. A010534, the square root of 83.
%K A379556 nonn,cons,easy
%O A379556 2,1
%A A379556 _Alonso del Arte_, Dec 25 2024