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
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).
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