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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 with 000 and 1 with 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 with 000 and 1 with 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 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 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 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

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Last modified October 24 04:14 EDT 2020. Contains 337975 sequences. (Running on oeis4.)