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A286841 One of the two successive approximations up to 13^n for 13-adic integer sqrt(-1). Here the 8 (mod 13) case (except for n=0). 15
0, 8, 99, 1958, 28322, 228249, 2827300, 55922199, 808904403, 9781942334, 52199939826, 603633907222, 11356596271444, 11356596271444, 1828607235824962, 37264994707118563, 651495710876207647, 5974828584341646375, 49226908181248336040 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..899

Wikipedia, Hensel's Lemma.

FORMULA

If n > 0, a(n) = 13^n - A286840(n).

a(0) = 0 and a(1) = 8, a(n) = a(n-1) + 4 * (a(n-1)^2 + 1) mod 13^n for n > 1.

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 A286841(n)

  A(8, 13, n)

end

p A286841(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 a286841(n): return A(8, 13, n)

print a286841(100) # Indranil Ghosh, Aug 03 2017, after Ruby

(PARI) a(n) = if (n, 13^n - truncate(sqrt(-1+O(13^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 this sequence (p=13), A286877 and A286878 (p=17).

Cf. A286839.

Sequence in context: A230343 A293145 A305919 * A316870 A181034 A324067

Adjacent sequences:  A286838 A286839 A286840 * A286842 A286843 A286844

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 01 2017

STATUS

approved

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Last modified February 22 13:49 EST 2020. Contains 332136 sequences. (Running on oeis4.)