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A290374 10-adic integer x = ...7057 satisfying x^5 = x. 5
7, 5, 0, 7, 7, 0, 2, 9, 0, 8, 1, 4, 3, 2, 5, 9, 5, 3, 6, 9, 1, 7, 1, 8, 7, 2, 0, 7, 3, 6, 9, 6, 1, 3, 3, 3, 7, 3, 3, 2, 8, 6, 5, 5, 4, 6, 7, 9, 1, 6, 8, 3, 2, 2, 4, 3, 3, 3, 1, 5, 0, 2, 4, 3, 0, 1, 9, 2, 0, 9, 6, 9, 5, 6, 1, 0, 0, 7, 2, 0, 4, 6, 6, 2, 9, 3, 5, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also x^2 = A091661.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..9999

FORMULA

p = A120817 = ...186432, q = A018247 = ...890625, x = p + q = ...077057.

EXAMPLE

     7^5 -    7 == 0 mod 10,

    57^5 -   57 == 0 mod 10^2,

    57^5 -   57 == 0 mod 10^3,

  7057^5 - 7057 == 0 mod 10^4.

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 A290374(n)

  str = (P(n) + Q(5, n)).to_s.reverse

  (0..n).map{|i| str[i].to_i}

end

p A290374(100)

CROSSREFS

x^5 = x: A120817 (...6432), A120818 (...3568), A290372 (...5807), A290373 (...2943), this sequence (...7057), A290375 (...4193).

Cf. A091661, A018247.

Sequence in context: A144923 A184908 A197519 * A202350 A096435 A021855

Adjacent sequences:  A290371 A290372 A290373 * A290375 A290376 A290377

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Jul 28 2017

STATUS

approved

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Last modified May 26 15:29 EDT 2019. Contains 323597 sequences. (Running on oeis4.)