A245645 - OEIS

%I #32 Jan 05 2025 19:51:40

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

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

%U 5,1,4,0,3,0,5,5,9,1,4,4,5,5,0,0,8,7,3,4,4,5,7,2,2,9,8,8,5,4,1,2,8

%N Decimal expansion of the common value of A and B in Daniel Shanks' "incredible identity" A = B.

%C See the Spohn reference for a generalization of this equality. - _Joerg Arndt_, May 01 2016

%D Henri Cohen, A Course in Computational Algebraic Number Theory, 3., corr. print., Springer-Verlag Berlin Heidelberg New York, 1996, Exercise 7 for Chapter 4, page 218.

%H Vincenzo Librandi, <a href="/A245645/b245645.txt">Table of n, a(n) for n = 1..1000</a>

%H Daniel Shanks, Incredible Identities, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-3/shanks-a.pdf">Part 1</a>, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/12-3/shanks-b.pdf">Part 2</a>, The Fibonacci Quarterly 12, no. 3 (1974):271, 280.

%H William G. Spohn, Jr., <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/14-1/letter1.pdf">Letter to the editor</a>, The Fibonacci Quarterly 14, no. 1 (1976).

%H Robert Allen Supencheck, <a href="https://doi.org/10.31979/etd.ux7a-p7hs">Some examples in low-dimensional algebraic number theory</a>, 1990; see chapter 1.

%F Equals A = sqrt(5) + sqrt(22 + 2*sqrt(5)),

%F Equals B = sqrt(11 + 2*sqrt(29)) + sqrt(16 - 2*sqrt(29) + 2*sqrt(55 - 10*sqrt(29))).

%F The minimal polynomial of both A and B is x^4 - 54*x^2 - 40*x + 269.

%e 7.3811759408956579709872668754651303326656461102953475776191021866181514...

%t RealDigits[Sqrt[5] + Sqrt[22 + 2*Sqrt[5]], 10, 101] // First

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jul 28 2014