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 A309614 Digits of the 10-adic integer (31/9)^(1/3). 3
 9, 1, 9, 8, 8, 1, 3, 3, 5, 8, 3, 9, 6, 0, 0, 9, 0, 6, 1, 9, 2, 8, 3, 4, 4, 7, 9, 1, 1, 5, 3, 2, 0, 1, 6, 9, 3, 2, 9, 2, 5, 9, 4, 0, 0, 4, 7, 9, 3, 2, 1, 0, 2, 1, 2, 7, 8, 7, 9, 2, 5, 1, 1, 5, 6, 3, 9, 3, 1, 7, 8, 5, 7, 1, 3, 2, 9, 4, 2, 5, 0, 2, 2, 4, 1, 5, 4, 0, 4, 2, 1, 5, 2, 0, 5, 5, 6, 2, 0, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 7 * (9 * b(n-1)^3 - 31) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. EXAMPLE 9^3 == 9      (mod 10).       19^3 == 59     (mod 10^2).      919^3 == 559    (mod 10^3).     8919^3 == 5559   (mod 10^4).    88919^3 == 55559  (mod 10^5).   188919^3 == 555559 (mod 10^6). PROG (PARI) N=100; Vecrev(digits(lift(chinese(Mod((31/9+O(2^N))^(1/3), 2^N), Mod((31/9+O(5^N))^(1/3), 5^N)))), N) (Ruby) def A309614(n)   ary = [9]   a = 9   n.times{|i|     b = (a + 7 * (9 * a ** 3 - 31)) % (10 ** (i + 2))     ary << (b - a) / (10 ** (i + 1))     a = b   }   ary end p A309614(100) CROSSREFS Cf. A309595, A309600. Sequence in context: A154697 A187368 A193670 * A154220 A133919 A145078 Adjacent sequences:  A309611 A309612 A309613 * A309615 A309616 A309617 KEYWORD nonn,base AUTHOR Seiichi Manyama, Aug 10 2019 STATUS approved

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Last modified September 20 16:50 EDT 2021. Contains 347586 sequences. (Running on oeis4.)