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A290375 10-adic integer x = ...4193 satisfying x^5 = x. 5
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

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

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).

Cf. A091661, A120818.

Sequence in context: A103556 A254348 A168399 * A245081 A010631 A019665

Adjacent sequences:  A290372 A290373 A290374 * A290376 A290377 A290378

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Jul 28 2017

STATUS

approved

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Last modified November 14 17:47 EST 2019. Contains 329126 sequences. (Running on oeis4.)