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 A005265 a(1)=3, b(n)=Product_{k=1..n} a(k), a(n+1)=smallest prime factor of b(n)-1. (Formerly M2246) 47
 3, 2, 5, 29, 11, 7, 13, 37, 32222189, 131, 136013303998782209, 31, 197, 19, 157, 17, 8609, 1831129, 35977, 508326079288931, 487, 10253, 1390043, 18122659735201507243, 25319167, 9512386441, 85577, 1031, 3650460767, 107, 41, 811, 15787, 89, 68168743, 4583, 239, 1283, 443, 902404933, 64775657, 2753, 23, 149287, 149749, 7895159, 79, 43, 1409, 184274081, 47, 569, 63843643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suggested by Euclid's proof that there are infinitely many primes. 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 Sean A. Irvine, Table of n, a(n) for n = 1..61 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. OEIS wiki, OEIS sequences needing factors S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. Applications, 8 (1993), 23-32. (Annotated scanned copy) MAPLE a :=n-> if n = 1 then 3 else numtheory:-divisors(mul(a(i), i = 1 .. n-1)-1)[2] fi:seq(a(n), n=1..15); # Robert FERREOL, Sep 25 2019 PROG (PARI) lpf(n)=factor(n)[1, 1] \\ better code exists, usually best to code in C and import print1(A=3); for(n=2, 99, a=lpf(A); print1(", "a); A*=a) \\ Charles R Greathouse IV, Apr 07 2020 CROSSREFS Cf. A000945, A000946, A005266, A084599. Essentially the same as A084598. Sequence in context: A085973 A302854 A248243 * A005266 A005267 A209269 Adjacent sequences:  A005262 A005263 A005264 * A005266 A005267 A005268 KEYWORD nonn,nice,hard AUTHOR STATUS approved

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Last modified June 5 11:52 EDT 2020. Contains 334840 sequences. (Running on oeis4.)