

A176594


a(n) = 5^(2^n).


4



5, 25, 625, 390625, 152587890625, 23283064365386962890625, 542101086242752217003726400434970855712890625, 293873587705571876992184134305561419454666389193021880377187926569604314863681793212890625
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OFFSET

0,1


COMMENTS

Also the hypotenuse of primitive Pythagorean triangles obtained by repeated application of basic formula c(n)=p(n)^2+q(n)^2 starting p(0)=2, q(0)=1, see A100686, A098122. Example: a(2)=25 since starting (2,1) gives Pythagorean triple (3,4,5) using (3,4) as new generators gives triple (7,24,25) hypotenuse 25=a(2).  Carmine Suriano, Feb 04 2011


LINKS

Table of n, a(n) for n=0..7.


FORMULA

a(n) = A165423(n+3).
a(n+1) = a(n)^2 with a(0)=5.
a(n1) = (Im((2+i)^(2^n))^2 + Re((2+i)^(2^n))^2)^(1/2).  Carmine Suriano, Feb 04 2011


PROG

(PARI) a(n) = 5^(2^n); \\ Michel Marcus, Jan 26 2016


CROSSREFS

Cf. A185457, A120905, A139011.  Carmine Suriano, Feb 04 2011
Sequence in context: A067270 A215118 A218150 * A274463 A279835 A169652
Adjacent sequences: A176591 A176592 A176593 * A176595 A176596 A176597


KEYWORD

nonn


AUTHOR

Vincenzo Librandi, Apr 21 2010


EXTENSIONS

Offset corrected by R. J. Mathar, Jun 18 2010


STATUS

approved



