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A290375 10-adic integer x = ...4193 satisfying x^5 = x. 7
3, 9, 1, 4, 0, 7, 3, 3, 3, 8, 1, 4, 6, 9, 9, 2, 5, 1, 8, 8, 5, 7, 3, 1, 2, 1, 2, 6, 7, 5, 8, 3, 8, 4, 8, 8, 4, 5, 4, 9, 7, 7, 0, 9, 3, 0, 7, 8, 2, 5, 2, 7, 7, 7, 7, 8, 2, 4, 1, 2, 1, 4, 7, 5, 1, 9, 3, 0, 3, 5, 5, 1, 4, 1, 6, 9, 1, 3, 4, 7, 4, 9, 3, 3, 0, 0, 8, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Also x^2 = A091661.
LINKS
FORMULA
p = A120818 = ...813568, q = A018247 = ...890625, x = p + q = ...704193.
EXAMPLE
3^5 - 3 == 0 mod 10,
93^5 - 93 == 0 mod 10^2,
193^5 - 193 == 0 mod 10^3,
4193^5 - 4193 == 0 mod 10^4.
From Seiichi Manyama, Aug 01 2019: (Start)
8^(5^0) + 5^(2^0) == 3 mod 10,
8^(5^1) + 5^(2^1) == 93 mod 10^2,
8^(5^2) + 5^(2^2) == 193 mod 10^3,
8^(5^3) + 5^(2^3) == 4193 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
}
}
s2
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 A290375(n)
str = (P(n) + Q(5, n)).to_s.reverse
(0..n).map{|i| str[i].to_i}
end
p A290375(100)
CROSSREFS
x^5 = x: A120817 (...6432), A120818 (...3568), A290372 (...5807), A290373 (...2943), A290374 (...7057), this sequence (...4193).
Sequence in context: A103556 A254348 A168399 * A245081 A010631 A355926
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.)