OFFSET
0,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Peter Bala, Using Chebyshev polynomials to find the p-adic square roots of 2 and 3, Dec 2022.
FORMULA
a(n) = 6 - A051277(n) for n > 0.
Equals the 7-adic limit as n -> oo of 2*T(7^n,2) = the 7-adic limit as n -> oo of (2 + sqrt(3))^(7^n) + (2 - sqrt(3))^(7^n), where T(n,x) denotes the n-th Chebyshev polynomial of the first kind. - Peter Bala, Nov 20 2022
MAPLE
t := proc(n) option remember; if n = 1 then 4 else irem(t(n-1)^7 - 7*t(n-1)^5 + 14*t(n-1)^3 - 7*t(n-1), 7^n) end if; end:
convert(t(100), base, 7); # Peter Bala, Nov 20 2022
PROG
(Ruby)
require 'OpenSSL'
def f_a(ary, a)
(0..ary.size - 1).inject(0){|s, i| s + ary[i] * a ** i}
end
def df(ary)
(1..ary.size - 1).map{|i| i * ary[i]}
end
def A(c_ary, k, m, n)
x = OpenSSL::BN.new((-f_a(df(c_ary), k)).to_s).mod_inverse(m).to_i % m
f_ary = c_ary.map{|i| x * i}
f_ary[1] += 1
d_ary = []
ary = [0]
a, mod = k, m
(n + 1).times{|i|
b = a % mod
d_ary << (b - ary[-1]) / m ** i
ary << b
a = f_a(f_ary, b)
mod *= m
}
d_ary
end
def A290558(n)
A([-2, 0, 1], 4, 7, n)
end
p A290558(100)
(PARI) { my(v=Vecrev( digits( truncate( (2+O(7^100))^(1/2) ), 7) )); vector(#v, k, 6-v[k]+(k==1)) } \\ Joerg Arndt, Aug 06 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 05 2017
STATUS
approved