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A193689
Even semiprime equivalent to the Euclid-Mullin sequence: a(1) = 4, a(n) = smallest semiprime divisor of product of previous terms plus 2.
0
4, 6, 26, 626, 34, 4762, 94, 10, 59450441556482, 37219202, 226, 14, 22, 359948158, 141142, 957030986, 82, 926, 46, 38, 86, 158, 262, 1126, 589928909976251551945088438, 4486, 2434, 62, 12398, 2367240322, 2942, 10430585378, 218, 394, 122, 74, 1042, 19862, 11197742711219732052345406
OFFSET
1,1
COMMENTS
Except for 4, all terms are guaranteed to be squarefree.
EXAMPLE
a(5) = 34 because the previous terms being 4, 6, 26 and 626, their product is 390624, and 390624 + 2 = 2 * 17 * 11489, the least semiprime divisor of which is 2 * 17 = 34.
MATHEMATICA
smallestPrimeFactor[n_] := FactorInteger[n][[1, 1]]; semiprimePart[n_] := Module[{p = smallestPrimeFactor[n]}, p*smallestPrimeFactor[n/p]]; a = {4}; Do[AppendTo[a, semiprimePart[2 + Times @@ a]], {15}]; a (* T. D. Noe, Aug 02 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Amiram Eldar, Feb 24 2021
STATUS
approved