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 A005266 a(1)=3, b(n)=Product_{k=1..n} a(k), a(n+1)=largest prime factor of b(n)-1. (Formerly M2247) 43
 3, 2, 5, 29, 79, 68729, 3739, 6221191, 157170297801581, 70724343608203457341903, 46316297682014731387158877659877, 78592684042614093322289223662773, 181891012640244955605725966274974474087, 547275580337664165337990140111772164867508038795347198579326533639132704344301831464707648235639448747816483406685904347568344407941 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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] REFERENCES 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. LINKS R. K. Guy and R. Nowakowski, Discovering primes with Euclid, Research Paper No. 260 (Nov 1974), The University of Calgary Department of Mathematics, Statistics and Computing Science. Des MacHale, Infinitely many proofs that there are infinitely many primes, Math. Gazette, 97 (No. 540, 2013), 495-498. S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. Applications, 8 (1993), 23-32. (Annotated scanned copy) MAPLE with(numtheory): a:= proc(n) option remember;       `if`(n=1, 3, max(factorset(mul(a(i), i=1..n-1)-1)[]))     end: seq(a(n), n=1..10);  # Alois P. Heinz, Sep 26 2013 MATHEMATICA a[0] = 3; a[n_] := a[n] = Block[{p = Times @@ (a[#] & /@ Range[0, n - 1]) - 1}, FactorInteger[p][[-1, 1]]]; Array[a, 13] (* Robert G. Wilson v, Sep 26 2013 *) CROSSREFS Cf. A000945, A000946, A005265. Essentially the same as A084599. Sequence in context: A302854 A248243 A005265 * A005267 A209269 A244823 Adjacent sequences:  A005263 A005264 A005265 * A005267 A005268 A005269 KEYWORD nonn,nice,hard AUTHOR EXTENSIONS a(14) from Joe K. Crump (joecr(AT)carolina.rr.com), Jul 26, 2000 STATUS approved

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Last modified May 28 11:40 EDT 2020. Contains 334681 sequences. (Running on oeis4.)