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A063006 Coefficients in a 10-adic square root of 1. 9
1, 5, 7, 8, 1, 2, 4, 7, 5, 3, 6, 1, 0, 8, 4, 7, 8, 4, 5, 1, 2, 5, 4, 0, 0, 6, 7, 6, 8, 7, 1, 9, 9, 1, 8, 7, 7, 0, 2, 8, 3, 5, 3, 5, 1, 3, 5, 1, 5, 8, 8, 8, 9, 9, 7, 7, 3, 2, 7, 2, 8, 3, 8, 0, 8, 9, 6, 6, 6, 5, 7, 8, 9, 1, 2, 0, 8, 9, 2, 2, 1, 4, 9, 3, 0, 6, 6, 3, 8, 7, 1, 6, 3, 5, 8, 9, 3, 9, 0, 2, 9, 1, 2, 7, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

10-adic integer x=.....86760045215487480163574218751 satisfying x^3=x.

A "bug" in the decimal enumeration system: another square root of 1.

Let a,b be integers defined in A018247, A018248 satisfying a^2=a,b^2=b, obviously a^3=a,b^3=b; let c,d,e,f be integers defined in A091661, A063006, A091663, A091664 then c^3=c, d^3=d, e^3=e, f^3=f, c+d=1, a+e=1, b+f=1, b+c=a, d+f=e, a+f=c, a=f+1, b=e+1, cd=-1, af=-1, gh=-1 where -1=.....999999999. - Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004

What about the 10-adic square roots of -1, -2, -3, 2, 3, 4, ... ? They do not exist, unless the square really is a square (+1, +4, +9, +16, ...). Then there's a nontrivial square root; for example, sqrt(4)=...44002229693692923584436016426479909569025039672851562498. - Don Reble, Apr 25 2006

REFERENCES

K. Mahler, Introduction to p-Adic Numbers and Their Functions, Cambridge, 1973.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..9999

FORMULA

(a_0 + a_1*10 + a_2*10^2 + a_3*10^3 + ... )^2 = 1 + 0*10 + 0*10^2 + 0*10^3 + ...

For n > 0, a(n) = 9 - A091661(n).

EXAMPLE

...4218751^2 = ...0000001

MATHEMATICA

To calculate c, d, e, f use Mathematica algorithms for a, b and equations: c=a-b, d=1-c, e=b-1, f=a-1. - Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004

CROSSREFS

Another 10-adic root of 1 is given by A091661.

Cf. A075693.

Sequence in context: A266712 A021177 A091662 * A135096 A153104 A233527

Adjacent sequences:  A063003 A063004 A063005 * A063007 A063008 A063009

KEYWORD

base,nonn,nice,easy

AUTHOR

Robert Lozyniak (11(AT)onna.com), Aug 03 2001

EXTENSIONS

More terms from Vladeta Jovovic, Aug 11 2001

STATUS

approved

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Last modified April 21 23:52 EDT 2021. Contains 343156 sequences. (Running on oeis4.)