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A286840 One of the two successive approximations up to 13^n for 13-adic integer sqrt(-1). Here the 5 (mod 13) case (except for n=0). 16
0, 5, 70, 239, 239, 143044, 1999509, 6826318, 6826318, 822557039, 85658552023, 1188526486815, 11941488851037, 291518510320809, 2108769149874327, 13920898306972194, 13920898306972194, 2675587335039691558, 63228498770709057089, 513050126578538629605 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..897

Wikipedia, Hensel's Lemma.

FORMULA

a(0) = 0 and a(1) = 5, a(n) = a(n-1) + 9 * (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 A286840(n)

  A(5, 13, n)

end

p A286840(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 a286840(n): return A(5, 13, n)

print a286840(100) # Indranil Ghosh, Aug 03 2017, after Ruby

(PARI) a(n) = truncate(sqrt(-1+O(13^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), this sequence and A286841 (p=13), A286877 and A286878 (p=17).

Cf. A034944, A286838.

Sequence in context: A299318 A051538 A218709 * A034944 A064046 A256235

Adjacent sequences:  A286837 A286838 A286839 * A286841 A286842 A286843

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Aug 01 2017

STATUS

approved

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Last modified February 23 16:19 EST 2020. Contains 332176 sequences. (Running on oeis4.)