A005265 - OEIS

A005265

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)

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

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

N. J. A. Sloane

STATUS

approved