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A071989 a(n) = n-th decimal digit of the fractional part of the square root of the n-th nonsquare number (A000037). 2
4, 3, 6, 4, 5, 7, 6, 9, 5, 4, 7, 7, 6, 8, 3, 3, 0, 4, 5, 9, 8, 3, 3, 0, 8, 9, 6, 2, 4, 1, 0, 4, 4, 0, 6, 7, 9, 5, 1, 7, 4, 1, 3, 5, 7, 5, 7, 7, 4, 8, 8, 9, 5, 0, 5, 0, 6, 5, 1, 7, 3, 3, 9, 9, 7, 7, 6, 1, 4, 9, 9, 2, 7, 8, 5, 8, 4, 9, 4, 5, 4, 2, 8, 0, 2, 1, 7, 7, 4, 7, 4, 8, 1, 8, 4, 5, 7, 5, 8, 0, 0, 0, 1, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Regarded as a decimal fraction, 0.43645769547768330... is likely to be an irrational number.

REFERENCES

Martin Aigner & Günter M. Ziegler, Proofs from THE BOOK, Second Edition, Springer-Verlag, Berlin Heidelberg NY, Section of Analysis, Chptr 15, "Sets, function, and the continuum hypothesis", 2000, pp. 87-98.

Georg Cantor, Über eine Eigenschaft des Inbegriffes aller reellen Zahlen ("On the Characteristic Property of All Real Numbers").

Timothy Gowers, Editor, with June Barrow-Green & Imre Leader, Assc. Editors, The Princeton Companion to Mathematics, Princeton Un. Press, Princeton & Oxford, 2008, pp. 171 & 779.

Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §7.5 Transfinite Numbers, pp. 257-262.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Tom Schaffter, Cantor's Diagonal Argument: Proof and Paradox

Richard Lipton, Gödel's Lost Letter and P=NP

Luke Mastin, 19th Century Mathematics - Cantor

Eric Weisstein's World of Mathematics, Cantor Diagonal Method

Wikipedia, Cantor's diagonal argument

FORMULA

The n-th nonsquare number is m(n) = n + ( sqrt( n + sqrt(n)).

EXAMPLE

Sqrt(2)=1.4142135... -> the 1st decimal digit is 4,

sqrt(3)=1.7320508... -> the 2nd decimal digit is 3,

sqrt(5)=2.2360679... -> the 3rd decimal digit is 6,

sqrt(6)=2.4494897... -> the 4th decimal digit is 4, etc.

MATHEMATICA

q[n_] := (m = Floor[n + Sqrt[n + Sqrt[n]]]; Floor[ Mod[ 10^n*Sqrt[m], 10]]); Table[ q[n], {n, 1, 105}]

CROSSREFS

Cf. A000037, A071901, A216251.

Sequence in context: A228780 A333328 A109339 * A290278 A300894 A328258

Adjacent sequences:  A071986 A071987 A071988 * A071990 A071991 A071992

KEYWORD

base,nonn

AUTHOR

Robert G. Wilson v, Jun 17 2002

STATUS

approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)