login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A245645 Decimal expansion of the common value of A and B in Daniel Shanks' "incredible identity" A = B. 1
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, 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, 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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See the Spohn reference for a generalization of this equality. - Joerg Arndt, May 01 2016

REFERENCES

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.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Daniel Shanks, Incredible Identities, Part 1, Part 2, The Fibonacci Quarterly 12, no. 3 (1974):271, 280.

William G. Spohn, Jr., Letter to the editor, The Fibonacci Quarterly 14, no. 1 (1976).

Robert Allen Supencheck, Some examples in low-dimensional algebraic number theory, 1990; see chapter 1.

FORMULA

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

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

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

EXAMPLE

7.3811759408956579709872668754651303326656461102953475776191021866181514...

MATHEMATICA

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

CROSSREFS

Sequence in context: A166201 A248281 A111197 * A335994 A115411 A019726

Adjacent sequences:  A245642 A245643 A245644 * A245646 A245647 A245648

KEYWORD

nonn,cons,easy

AUTHOR

Jean-François Alcover, Jul 28 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)