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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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

Crossrefs

Cf. A290557.

Programs

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

Python

def a034945(n):
    ary=[0]
    a, mod=3, 7
    while len(ary) - 1Indranil Ghosh, Aug 03 2017, after Ruby

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