login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225406 Digits of the 10-adic integer 9^(1/3). 8
9, 6, 5, 0, 6, 6, 3, 4, 8, 6, 6, 0, 4, 8, 5, 4, 5, 9, 4, 5, 1, 1, 9, 4, 0, 6, 0, 8, 1, 3, 7, 0, 6, 6, 9, 4, 8, 3, 9, 9, 3, 0, 2, 4, 2, 0, 3, 5, 9, 8, 6, 5, 5, 0, 9, 6, 7, 7, 4, 8, 0, 7, 4, 6, 1, 0, 3, 2, 9, 8, 5, 8, 2, 1, 5, 7, 0, 9, 0, 9, 8, 8, 1, 6, 0, 6, 8, 6, 0, 3, 9, 5, 0, 9, 9, 5, 6, 5, 3, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

FORMULA

p = ...660569, q = A225409 = ...339431, p + q = 0. - Seiichi Manyama, Aug 04 2019

Define the sequence {b(n)} by the recurrence b(0) = 0 and b(1) = 9, b(n) = b(n-1) + 3 * (b(n-1)^3 - 9) mod 10^n for n > 1, then a(n) = (b(n+1) - b(n))/10^n. - Seiichi Manyama, Aug 13 2019

EXAMPLE

       9^3 == 9 (mod 10).

      69^3 == 9 (mod 10^2).

     569^3 == 9 (mod 10^3).

     569^3 == 9 (mod 10^4).

   60569^3 == 9 (mod 10^5).

  660569^3 == 9 (mod 10^6).

MAPLE

op([1, 3], padic:-rootp((x)^3  -9,  10, 101)); # Robert Israel, Aug 04 2019

PROG

(PARI) n=0; for(i=1, 100, m=9; for(x=0, 9, if(((n+(x*10^(i-1)))^3)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break)))

(PARI) Vecrev(digits(truncate(-(-9+O(10^100))^(1/3)))) \\ Seiichi Manyama, Aug 04 2019

(PARI) N=100; Vecrev(digits(lift(chinese(Mod((9+O(2^N))^(1/3), 2^N), Mod((9+O(5^N))^(1/3), 5^N)))), N) \\ Seiichi Manyama, Aug 04 2019

(Ruby)

def A225406(n)

  ary = [9]

  a = 9

  n.times{|i|

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

    ary << (b - a) / (10 ** (i + 1))

    a = b

  }

  ary

end

p A225406(100) # Seiichi Manyama, Aug 13 2019

CROSSREFS

Cf. A309600.

Digits of 10-adic integers:

A153042 ((-1/9)^(1/3));

A225409 (  (-9)^(1/3));

A225412 ( (1/9)^(1/3)).

Sequence in context: A154183 A200138 A196772 * A247040 A019942 A102047

Adjacent sequences:  A225403 A225404 A225405 * A225407 A225408 A225409

KEYWORD

nonn,base

AUTHOR

Aswini Vaidyanathan, May 07 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 4 02:21 EDT 2020. Contains 335436 sequences. (Running on oeis4.)