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A005266
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a(1)=3, b(n)=Product_{k=1..n} a(k), a(n+1)=largest prime factor of b(n)-1.
(Formerly M2247)
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39
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3, 2, 5, 29, 79, 68729, 3739, 6221191, 157170297801581, 70724343608203457341903, 46316297682014731387158877659877, 78592684042614093322289223662773, 181891012640244955605725966274974474087, 547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941
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OFFSET
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0,1
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COMMENTS
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Suggested by Euclid's proof that there are infinitely many primes.
a(15) requires completing the factorization: 13 * 67 * 14479 * 167197 * 924769 * 2688244927 * 888838110930755119 * 14372541055015356634061816579965403 * C211 where C211=6609133306626483634448666494646737799624640616060730302142187545405582531010390290502001156883917023202671554510633460047901459959959325342475132778791495112937562941066523907603281586796876335607258627832127303 [From Sean A. Irvine, Nov 10 2009]
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REFERENCES
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R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Delta (Waukesha), Vol. 5, pp. 49-63, 1975.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. Applications, 8 (1993), 23-32.
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LINKS
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Table of n, a(n) for n=0..13.
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CROSSREFS
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Cf. A000945, A000946, A005265.
Essentially the same as A084599.
Sequence in context: A103938 A085973 A005265 * A005267 A209269 A016460
Adjacent sequences: A005263 A005264 A005265 * A005267 A005268 A005269
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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a(14) from Joe K. Crump (joecr(AT)carolina.rr.com), Jul 26, 2000
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STATUS
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approved
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