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A286877 One of the two successive approximations up to 17^n for 17-adic integer sqrt(-1). Here the 4 (mod 17) case (except for n=0). 7
0, 4, 38, 2928, 27493, 1029745, 23747457, 313398285, 3596107669, 94280954402, 450044583893, 28673959190179, 28673959190179, 3524407382568745, 13428985415474682, 13428985415474682, 42949774758062711577, 91610966633729580058, 6709533061724423693474 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

x   = ...GC5A24,

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

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..813

Wikipedia, Hensel's Lemma.

FORMULA

a(0) = 0 and a(1) = 4, a(n) = a(n-1) + 2 * (a(n-1)^2 + 1) mod 17^n for n > 1.

EXAMPLE

a(1) = (   4)_17 = 4,

a(2) = (  24)_17 = 38,

a(3) = ( A24)_17 = 2928,

a(4) = (5A24)_17 = 27493.

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 A286877(n)

  A(4, 17, n)

end

p A286877(100)

(Python)

def A(k, m, n):

      ary=[0]

      a, mod = k, m

      for i in xrange(n):

          b=a%mod

          ary+=[b, ]

          a=b**m

          mod*=m

      return ary

def a286877(n): return A(4, 17, n)

print a286877(100) # Indranil Ghosh, Aug 03 2017

(PARI) a(n) = truncate(sqrt(-1+O(17^n))); \\ 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), this sequence and A286878 (p=17).

Sequence in context: A131591 A030259 A218710 * A018860 A016484 A106127

Adjacent sequences:  A286874 A286875 A286876 * A286878 A286879 A286880

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 02 2017

STATUS

approved

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Last modified April 22 11:46 EDT 2019. Contains 322330 sequences. (Running on oeis4.)