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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 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 A355926 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 February 25 10:53 EST 2024. Contains 370323 sequences. (Running on oeis4.)