OFFSET
0,2
COMMENTS
Dirichlet proved that for every prime p there exists at least one prime of the form k*p + 1, hence the sequence is infinite.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..100
Thomas Bloom, Problem 695, Erdős Problems.
Lejeune-Dirichlet, There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime, arXiv:0808.1408 [math.HO], 2008-2014 (original 1837, translated from German).
Erdős problems database contributors, Erdős problem database, see no. 695
Amarnath Murthy, On the divisors of Smarandache Unary Sequence. Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000, page 184.
EXAMPLE
59 = 2*29 + 1; 709 = 12*59 + 1.
MATHEMATICA
a[1] = 2; a[n_] := a[n] = Block[{k = 1, p = a[n - 1]}, While[ !PrimeQ[k*p + 1], k++ ]; k*p + 1]; Table[ a[n], {n, 21}] (* Robert G. Wilson v, Nov 26 2004 *)
PROG
(PARI) for (n=0, 100, if (n>0, k=1; while (!isprime(k*a + 1), k++); a=k*a + 1, a=1); write("b061092.txt", n, " ", a)) \\ Harry J. Smith, Jul 17 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Apr 19 2001
EXTENSIONS
More terms from Patrick De Geest, May 29 2001
Edited by Charles R Greathouse IV, Aug 02 2010
STATUS
approved