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
KEYWORD
base,nonn
AUTHOR
Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004
STATUS
approved