0,1

It is an open question whether all terms of this sequence are square-free.

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

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 211, p. 61, Ellipses, Paris 2008.

S. W. Golomb, The evidence for Fortune's conjecture, Math. Mag. 54 (1981), 209-210.

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990.

F. Iacobescu, Smarandache partition type and other sequences, Bulletin of pure and applied sciences, Vol. 16E, No. 2, pp. 237-240.

H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

F. Smarandache, Properties of numbers, Arizona State University Special Collections, 1973.

I. Vardi, Computational Recreations in Mathematica, Addison-Wesley, 1991, sections 5.1 and 5.2.

S. Wagon, Mathematica in Action, Freeman, NY, 1991, p. 35.

T. D. Noe, Table of n, a(n) for n=0..100

Hisanori Mishima, Factorizations of many number sequences

Hisanori Mishima, Factorizations of many number sequences

M. L. Perez et al., eds., Smarandache Notions Journal

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.

Eric Weisstein's World of Mathematics, Fortunate Prime

R. G. Wilson v, Explicit factorizations

with(numtheory): A006862 := proc(n) local i; if n=0 then 2 else 1+product('ithprime(i)', 'i'=1..n); fi; end;

Table[Product[Prime[k], {k, 1, n}] + 1, {n, 1, 18}]

Equals A002110 + 1. Cf. A014545, A057588, A018239 (primes).

Sequence in context: A089359 A081947 A046972 this_sequence A038710 A073918 A096350

Adjacent sequences: A006859 A006860 A006861 this_sequence A006863 A006864 A006865

nonn,nice,easy

Simon Plouffe, N. J. A. Sloane (njas(AT)research.att.com).