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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 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 February 25 11:23 EST 2024. Contains 370325 sequences. (Running on oeis4.)