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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
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.
Sequence in context: A330274 A248197 A199291 * A362943 A011313 A319530
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.)