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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

%I

%S 1,5,325,85197125,1534774961612150361293125,

%T 8972304477322525702813810177861539421333393918862058319149818714344653125

%N 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.

%C The next term, a(6), has 202 digits and does not fit on one line.

%C This is the decimal representation of the terms of A292686 considered as binary numbers.

%C 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.

%F a(n+1) = (4^(3^n)+1)*a(n).

%F a(n) = Product_{k=0 .. n-1} (4^(3^k)+1).

%e 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.

%e 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.

%e 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.

%o (PARI) A292687(n)=prod(k=0,n-1,4^3^k+1)

%Y Cf. A292686 for the binary representation of a(n), and for more links, references and motivation.

%K nonn

%O 0,2

%A _M. F. Hasler_, Oct 20 2017

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Last modified April 19 21:01 EDT 2019. Contains 322291 sequences. (Running on oeis4.)