

A292687


a(n) = Product_{k=0 .. n1} (4^(3^k) + 1) = decimal value of the Sierpinskitype iteration result A292686(n) (replace 0 by 000 and 1 by 101) considered as a binary number.


2




OFFSET

0,2


COMMENTS

The next term, a(6), has 202 digits and does not fit on one line.
This is the decimal representation of the terms of A292686 considered as binary numbers.
To get a(n+1) from a(n), write a(n) in binary, replace digits 0 by 000 and 1 by 101, and convert back to decimal. Equivalently, consider the binary expansion of a(n) as base8 expansion, multiply it by 5, and convert back from octal to decimal.


LINKS

Table of n, a(n) for n=0..5.


FORMULA

a(n+1) = (4^(3^n)+1)*a(n).
a(n) = Product_{k=0 .. n1} (4^(3^k)+1).


EXAMPLE

a(0) = 1 is already written in binary; multiplied by 5 it yields 5, read in octal is the same as in decimal, a(1) = 5.
a(1) = 5 = 101[2] in binary; consider 101 in base 8 (or base 10), multiply by 5 to get 505, convert from octal to decimal to get a(2) = 5*8^2 + 5 = 325.
a(2) = 325 = 101000101[2] in binary; consider this in base 8 (or base 10), multiply by 5 to get 505000505, convert from octal to decimal to get a(2) = 325*8^6 + 325 = 85197125.


PROG

(PARI) A292687(n)=prod(k=0, n1, 4^3^k+1)


CROSSREFS

Cf. A292686 for the binary representation of a(n), and for more links, references and motivation.
Sequence in context: A274306 A053516 A085523 * A152425 A304017 A305365
Adjacent sequences: A292684 A292685 A292686 * A292688 A292689 A292690


KEYWORD

nonn


AUTHOR

M. F. Hasler, Oct 20 2017


STATUS

approved



