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A286878 One of the two successive approximations up to 17^n for 17-adic integer sqrt(-1). Here the 13 (mod 17) case (except for n=0). 13
0, 13, 251, 1985, 56028, 390112, 390112, 96940388, 3379649772, 24306922095, 1565949316556, 5597937117454, 553948278039582, 6380170650337192, 154948841143926247, 2848994066094341111, 5711417117604156904, 735629295252607184119, 7353551390343301297535 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...04B6ED,

x^2 = ...GGGGGG = -1.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..812

Wikipedia, Hensel's Lemma.

FORMULA

If n > 0, a(n) = 17^n - A286877(n).

a(0) = 0 and a(1) = 13, a(n) = a(n-1) + 15 * (a(n-1)^2 + 1) mod 17^n for n > 1.

EXAMPLE

a(1) = (   D)_17 = 13,

a(2) = (  ED)_17 = 251,

a(3) = ( 6ED)_17 = 1985,

a(4) = (B6ED)_17 = 56028.

PROG

(Ruby)

def A(k, m, n)

  ary = [0]

  a, mod = k, m

  n.times{

    b = a % mod

    ary << b

    a = b ** m

    mod *= m

  }

  ary

end

def A286878(n)

  A(13, 17, n)

end

p A286878(100)

(Python)

def A(k, m, n):

      ary=[0]

      a, mod = k, m

for i in range(n):

          b=a%mod

          ary+=[b, ]

          a=b**m

          mod*=m

      return ary

def a286878(n): return A(13, 17, n)

print a286878(100) # Indranil Ghosh, Aug 03 2017, after Ruby

(PARI) a(n) = if (n, 17^n-truncate(sqrt(-1+O(17^n))), 0); \\ Michel Marcus, Aug 04 2017

CROSSREFS

The two successive approximations up to p^n for p-adic integer sqrt(-1): A048898 and A048899 (p=5), A286840 and A286841 (p=13), A286877 and this sequence (p=17).

Sequence in context: A218315 A183416 A126422 * A106738 A332849 A001508

Adjacent sequences:  A286875 A286876 A286877 * A286879 A286880 A286881

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 02 2017

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)