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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)

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

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Sean A. Irvine added terms 54 through 61, May 21 2006

STATUS

approved

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Last modified October 17 12:01 EDT 2018. Contains 316279 sequences. (Running on oeis4.)