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 A091661 Coefficients in a 10-adic square root of 1. 13
 9, 4, 2, 1, 8, 7, 5, 2, 4, 6, 3, 8, 9, 1, 5, 2, 1, 5, 4, 8, 7, 4, 5, 9, 9, 3, 2, 3, 1, 2, 8, 0, 0, 8, 1, 2, 2, 9, 7, 1, 6, 4, 6, 4, 8, 6, 4, 8, 4, 1, 1, 1, 0, 0, 2, 2, 6, 7, 2, 7, 1, 6, 1, 9, 1, 0, 3, 3, 3, 4, 2, 1, 0, 8, 7, 9, 1, 0, 7, 7, 8, 5, 0, 6, 9, 3, 3, 6, 1, 2, 8, 3, 6, 4, 1, 0, 6, 0, 9, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 10-adic integer x=.....239954784512519836425781249 satisfying x^3 = x. 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. LINKS Seiichi Manyama, Table of n, a(n) for n = 0..9999 FORMULA For n>0, a(n) = 9 - A063006(n). 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. PROG (Ruby) def A(s, n) n.times{|i| m = 10 ** (i + 1) (0..9).each{|j| k = j * m + s if (k ** 2 - k) % (m * 10) == 0 s = k break end } } s end def A091661(n) str = (10 ** (n + 1) + A(5, n) - A(6, n)).to_s.reverse (0..n).map{|i| str[i].to_i} end p A091661(100) # Seiichi Manyama, Jul 31 2017 CROSSREFS Another 10-adic root of 1 is given by A063006. Cf. A018247, A018248. Sequence in context: A330274 A248197 A199291 * A362943 A011313 A319530 Adjacent sequences: A091658 A091659 A091660 * A091662 A091663 A091664 KEYWORD base,nonn AUTHOR Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004 STATUS approved

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Last modified February 25 10:20 EST 2024. Contains 370318 sequences. (Running on oeis4.)