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A005265
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a(1)=3, b(n) = Product_{k=1..n} a(k), a(n+1) is the smallest prime factor of b(n)-1.
(Formerly M2246)
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47
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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
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OFFSET
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1,1
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COMMENTS
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Suggested by Euclid's proof that there are infinitely many primes.
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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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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.
S. S. Wagstaff, Jr., Computing Euclid's primes, Bull. Institute Combin. Applications, 8 (1993), 23-32. (Annotated scanned copy)
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MAPLE
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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);
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PROG
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(PARI) lpf(n)=factor(n)[1, 1] \\ better code exists, usually best to code in C and import
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CROSSREFS
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KEYWORD
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nonn,nice,hard
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AUTHOR
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STATUS
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approved
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