|
|
A286878
|
|
One of the two successive approximations up to 17^n for 17-adic integer sqrt(-1). Here the 13 (mod 17) case (except for n=0).
|
|
13
|
|
|
0, 13, 251, 1985, 56028, 390112, 390112, 96940388, 3379649772, 24306922095, 1565949316556, 5597937117454, 553948278039582, 6380170650337192, 154948841143926247, 2848994066094341111, 5711417117604156904, 735629295252607184119, 7353551390343301297535
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
x = ...04B6ED,
x^2 = ...GGGGGG = -1.
|
|
LINKS
|
|
|
FORMULA
|
If n > 0, a(n) = 17^n - A286877(n).
a(0) = 0 and a(1) = 13, a(n) = a(n-1) + 15 * (a(n-1)^2 + 1) mod 17^n for n > 1.
|
|
EXAMPLE
|
a(1) = ( D)_17 = 13,
a(2) = ( ED)_17 = 251,
a(3) = ( 6ED)_17 = 1985,
a(4) = (B6ED)_17 = 56028.
|
|
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
A(13, 17, n)
end
(Python)
def A(k, m, n):
ary=[0]
a, mod = k, m
for i in range(n):
b=a%mod
ary.append(b)
a=b**m
mod*=m
return ary
def a286878(n): return A(13, 17, n)
(PARI) a(n) = if (n, 17^n-truncate(sqrt(-1+O(17^n))), 0); \\ Michel Marcus, Aug 04 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|