A034945 Successive approximations to 7-adic integer sqrt(2).

0, 3, 10, 108, 2166, 4567, 38181, 155830, 1802916, 24862120, 266983762, 1961835256, 5916488742, 19757775943, 116646786350, 9611769806236, 42844700375837, 275475214363044, 6789129606004840, 75182500718243698

Offset

0,2

References

K. Mahler, Introduction to p-Adic Numbers and Their Functions, Cambridge, 1973, p. 35.

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1010

Prog

(PARI) seq(n)={my(v=vector(n), i=1, k=0); while(i<#v, k++; my(t=truncate(sqrt(2 + O(7^k)))); if(t > v[i], i++; v[i]=t)); v} \\ Andrew Howroyd, Nov 03 2018
(Ruby)
def A034945(n)
  ary = [0]
  a, mod = 3, 7
  while ary.size - 1 < n
    b = a % mod
    ary << b if b != ary[-1]
    a = b * b + b - 2
    mod *= 7
  end
  ary
end
p A034945(100) # Seiichi Manyama, Aug 03 2017
(Python)
def a034945(n):
    ary=[0]
    a, mod=3, 7
    while len(ary) - 1<n:
        b=a%mod
        if b!=ary[-1]: ary.append(b)
        a=b**2 + b - 2
        mod*=7
    return ary
print(a034945(100)) # Indranil Ghosh, Aug 03 2017, after Ruby

Crossrefs

Cf. A290557.

Sequence in context: A048531 A073306 A290557 * A380789 A374868 A132480

Adjacent sequences: A034942 A034943 A034944 * A034946 A034947 A034948

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved