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A309600 Digits of the 10-adic integer (17/9)^(1/3). 36
7, 1, 6, 8, 7, 0, 3, 3, 3, 6, 5, 2, 7, 8, 7, 2, 6, 7, 1, 1, 0, 3, 3, 2, 4, 5, 6, 5, 3, 6, 5, 3, 3, 3, 7, 5, 2, 4, 7, 5, 0, 2, 9, 0, 6, 7, 0, 8, 8, 6, 6, 7, 0, 1, 2, 4, 5, 3, 2, 8, 6, 9, 7, 3, 1, 6, 6, 9, 5, 0, 1, 6, 4, 6, 8, 0, 3, 8, 5, 9, 6, 1, 3, 5, 3, 7, 9, 7, 2, 3, 6, 6, 9, 0, 0, 0, 5, 3, 7, 7, 2 (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) = 7, b(n) = b(n-1) + 3 * (9 * b(n-1)^3 - 17) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n.

EXAMPLE

      7^3 == 3      (mod 10).

     17^3 == 13     (mod 10^2).

    617^3 == 113    (mod 10^3).

   8617^3 == 1113   (mod 10^4).

  78617^3 == 11113  (mod 10^5).

  78617^3 == 111113 (mod 10^6).

PROG

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((17/9+O(2^N))^(1/3), 2^N), Mod((17/9+O(5^N))^(1/3), 5^N)))), N)

(Ruby)

def A309600(n)

  ary = [7]

  a = 7

  n.times{|i|

    b = (a + 3 * (9 * a ** 3 - 17)) % (10 ** (i + 2))

    ary << (b - a) / (10 ** (i + 1))

    a = b

  }

  ary

end

p A309600(100)

CROSSREFS

10-adic integer x.

A225404       (x^3 = ...000003).

A225405       (x^3 = ...000007).

A225406       (x^3 = ...000009).

A153042       (x^3 = ...111111).

this sequence (x^3 = ...111113).

A309601       (x^3 = ...111117).

A309602       (x^3 = ...111119).

A309603       (x^3 = ...222221).

A225410       (x^3 = ...222223).

A309604       (x^3 = ...222227).

A309605       (x^3 = ...222229).

A309606       (x^3 = ...333331).

A225402       (x^3 = ...333333).

A309569       (x^3 = ...333337).

A309570       (x^3 = ...333339).

A309595       (x^3 = ...444441).

A309608       (x^3 = ...444443).

A309609       (x^3 = ...444447).

A309610       (x^3 = ...444449).

A309611       (x^3 = ...555551).

A309612       (x^3 = ...555553).

A309613       (x^3 = ...555557).

A309614       (x^3 = ...555559).

A309640       (x^3 = ...666661).

A309641       (x^3 = ...666663).

A225411       (x^3 = ...666667).

A309642       (x^3 = ...666669).

A309643       (x^3 = ...777771).

A309644       (x^3 = ...777773).

A225401       (x^3 = ...777777).

A309645       (x^3 = ...777779).

A309646       (x^3 = ...888881).

A309647       (x^3 = ...888883).

A309648       (x^3 = ...888887).

A225412       (x^3 = ...888889).

A225409       (x^3 = ...999991).

A225408       (x^3 = ...999993).

A225407       (x^3 = ...999997).

Sequence in context: A060625 A145423 A019796 * A190264 A322663 A231927

Adjacent sequences:  A309597 A309598 A309599 * A309601 A309602 A309603

KEYWORD

nonn,base

AUTHOR

Seiichi Manyama, Aug 09 2019

STATUS

approved

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Last modified April 7 19:49 EDT 2020. Contains 333306 sequences. (Running on oeis4.)