|
|
A185457
|
|
a(n) = abs( Im((2+i)^(2^n)) ).
|
|
2
|
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The next term is too large to be displayed here.
Old name was: Leg of primitive Pythagorean triangle generated by repeated application of the basic formula y(n) = 2*x(n-1)*y(n-1), x(1)=2, y(1)=1.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = abs( Im((2+i)^(2^n)) ).
|
|
EXAMPLE
|
y(2)=24 since x(1)=3, y(1)=4 are the two legs of Pythagorean triangle obtained by p=2, q=1; second iteration p=3, q=4 gives 2*3*4=24.
|
|
MAPLE
|
a:= n-> abs(Im((2+I)^(2^n))):
|
|
MATHEMATICA
|
Table[Abs[Im[(2 + I)^(2^n)]], {n, 0, 10}] (* G. C. Greubel, Jul 07 2017 *)
|
|
PROG
|
(PARI) a(n) = abs(imag((2+I)^(2^n))); \\ Joerg Arndt, Apr 25 2013
(Python)
from sympy import im, I
def a(n): return abs(im((2 + I)**(2**n)))
|
|
CROSSREFS
|
Cf. A099456 ( imaginary part of (2+i)^n ).
|
|
KEYWORD
|
nonn,less
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|