Search: id:A006862
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%I A006862 M2698
%S A006862 2,3,7,31,211,2311,30031,510511,9699691,223092871,6469693231,
%T A006862 200560490131,7420738134811,304250263527211,13082761331670031,
%U A006862 614889782588491411,32589158477190044731,1922760350154212639071
%N A006862 Euclid numbers: 1 + product of first n consecutive primes.
%C A006862 It is an open question whether all terms of this sequence are square-free.
%C A006862 a(n) is the smallest x > 1 such that x^prime(n) == 1 mod(prime(i)) i=1,
               2,3,...,n-1 - Benoit Cloitre (benoit7848c(AT)orange.fr), May 30 2002
%D A006862 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, 
               Paris 2008.
%D A006862 S. W. Golomb, The evidence for Fortune's conjecture, Math. Mag. 54 (1981), 
               209-210.
%D A006862 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990.
%D A006862 F. Iacobescu, Smarandache partition type and other sequences, Bulletin 
               of pure and applied sciences, Vol. 16E, No. 2, pp. 237-240.
%D A006862 H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, 
               Vol. 8, No. 1-2-3, 1997, 170-183.
%D A006862 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006862 F. Smarandache, Properties of numbers, Arizona State University Special 
               Collections, 1973.
%D A006862 I. Vardi, Computational Recreations in Mathematica, Addison-Wesley, 1991, 
               sections 5.1 and 5.2.
%D A006862 S. Wagon, Mathematica in Action, Freeman, NY, 1991, p. 35.
%H A006862 T. D. Noe, <a href="b006862.txt">Table of n, a(n) for n=0..100</a>
%H A006862 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha102.htm">Factorizations of many number sequences</a>
%H A006862 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha103.htm">Factorizations of many number sequences</a>
%H A006862 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A006862 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EuclidNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A006862 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FortunatePrime.html">Fortunate Prime</a>
%H A006862 R. G. Wilson v, <a href="a38507.txt">Explicit factorizations</a>
%p A006862 with(numtheory): A006862 := proc(n) local i; if n=0 then 2 else 1+product('ithprime(i)',
               'i'=1..n); fi; end;
%t A006862 Table[Product[Prime[k], {k, 1, n}] + 1, {n, 1, 18}]
%Y A006862 Equals A002110 + 1. Cf. A014545, A057588, A018239 (primes).
%Y A006862 Sequence in context: A089359 A081947 A046972 this_sequence A038710 A073918 
               A096350
%Y A006862 Adjacent sequences: A006859 A006860 A006861 this_sequence A006863 A006864 
               A006865
%K A006862 nonn,nice,easy
%O A006862 0,1
%A A006862 Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).

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