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A290372 10-adic integer x = ...5807 satisfying x^5 = x. 7
7, 0, 8, 5, 9, 2, 6, 6, 6, 1, 8, 5, 3, 0, 0, 7, 4, 8, 1, 1, 4, 2, 6, 8, 7, 8, 7, 3, 2, 4, 1, 6, 1, 5, 1, 1, 5, 4, 5, 0, 2, 2, 9, 0, 6, 9, 2, 1, 7, 4, 7, 2, 2, 2, 2, 1, 7, 5, 8, 7, 8, 5, 2, 4, 8, 0, 6, 9, 6, 4, 4, 8, 5, 8, 3, 0, 8, 6, 5, 2, 5, 0, 6, 6, 9, 9, 1, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Also x^2 = A091661.
LINKS
FORMULA
p = A120817 = ...186432, q = A018247 = ...890625, x = p - q = ...295807.
EXAMPLE
7^5 - 7 == 0 mod 10,
7^5 - 7 == 0 mod 10^2,
807^5 - 807 == 0 mod 10^3,
5807^5 - 5807 == 0 mod 10^4.
From Seiichi Manyama, Aug 01 2019: (Start)
2^(5^0) - 5^(2^0) == 7 mod 10,
2^(5^1) - 5^(2^1) == 7 mod 10^2,
2^(5^2) - 5^(2^2) == 807 mod 10^3,
2^(5^3) - 5^(2^3) == 5807 mod 10^4. (End)
PROG
(Ruby)
def P(n)
s1, s2 = 2, 8
n.times{|i|
m = 10 ** (i + 1)
(0..9).each{|j|
k1, k2 = j * m + s1, (9 - j) * m + s2
if (k1 ** 5 - k1) % (m * 10) == 0 && (k2 ** 5 - k2) % (m * 10) == 0
s1, s2 = k1, k2
break
end
}
}
s1
end
def Q(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 A290372(n)
str = (10 ** (n + 1) + P(n) - Q(5, n)).to_s.reverse
(0..n).map{|i| str[i].to_i}
end
p A290372(100)
CROSSREFS
Sequence in context: A176015 A322910 A198939 * A190410 A283881 A178308
KEYWORD
nonn,base
AUTHOR
Seiichi Manyama, Jul 28 2017
STATUS
approved

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Last modified February 25 10:53 EST 2024. Contains 370323 sequences. (Running on oeis4.)