login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292687 a(n) = Product_{k=0 .. n-1} (4^(3^k) + 1) = decimal value of the Sierpinski-type iteration result A292686(n) (replace 0 by 000 and 1 by 101) considered as a binary number. 2
1, 5, 325, 85197125, 1534774961612150361293125, 8972304477322525702813810177861539421333393918862058319149818714344653125 (list; graph; refs; listen; history; text; internal format)
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 base-8 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 .. n-1} (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, n-1, 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 03:59 EDT 2019. Contains 321311 sequences. (Running on oeis4.)