A309600 - OEIS

A309600

Digits of the 10-adic integer (17/9)^(1/3).

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

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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