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A290373 10-adic integer x = ...2943 satisfying x^5 = x. 7
3, 4, 9, 2, 2, 9, 7, 0, 9, 1, 8, 5, 6, 7, 4, 0, 4, 6, 3, 0, 8, 2, 8, 1, 2, 7, 9, 2, 6, 3, 0, 3, 8, 6, 6, 6, 2, 6, 6, 7, 1, 3, 4, 4, 5, 3, 2, 0, 8, 3, 1, 6, 7, 7, 5, 6, 6, 6, 8, 4, 9, 7, 5, 6, 9, 8, 0, 7, 9, 0, 3, 0, 4, 3, 8, 9, 9, 2, 7, 9, 5, 3, 3, 7, 0, 6, 4, 8 (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 = ...922943.
EXAMPLE
3^5 - 3 == 0 mod 10,
43^5 - 43 == 0 mod 10^2,
943^5 - 943 == 0 mod 10^3,
2943^5 - 2943 == 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) == 43 mod 10^2,
8^(5^2) - 5^(2^2) == 943 mod 10^3,
8^(5^3) - 5^(2^3) == 2943 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 A290373(n)
str = (10 ** (n + 1) + P(n) - Q(5, n)).to_s.reverse
(0..n).map{|i| str[i].to_i}
end
p A290373(100)
CROSSREFS
Sequence in context: A246726 A019900 A329212 * A122791 A011429 A225409
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.)