A185457 a(n) = abs( Im((2+i)^(2^n)) ).

1, 4, 24, 336, 354144, 116749235904, 22940770664883067253376, 182503181432559739767250904458105698387204864

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

Alois P. Heinz, Table of n, a(n) for n = 0..11

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))):
seq(a(n), n=0..8);  # Alois P. Heinz, Apr 25 2013

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)))
print([a(n) for n in range(11)]) # Indranil Ghosh, Jul 08 2017

Crossrefs

Cf. A176594, A120905.

Cf. A099456 ( imaginary part of (2+i)^n ).

Sequence in context: A374386 A361054 A196687 * A024250 A167140 A010572

Adjacent sequences: A185454 A185455 A185456 * A185458 A185459 A185460

Keyword

nonn,less

Author

Carmine Suriano, Feb 04 2011

Extensions

Better name from Joerg Arndt, Apr 25 2013

Status

approved