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. - 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
KEYWORD
nonn,nice,hard
AUTHOR
EXTENSIONS
a(14) from Joe K. Crump (joecr(AT)carolina.rr.com), Jul 26 2000
STATUS
approved