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A063006 Coefficients in a 10-adic square root of 1. 10
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
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
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 February 25 11:23 EST 2024. Contains 370325 sequences. (Running on oeis4.)