A061092 a(0) = 1; for n>0, a(n) = smallest prime of the form k*a(n-1) + 1.

1, 2, 3, 7, 29, 59, 709, 2837, 22697, 590123, 1180247, 9441977, 169955587, 2719289393, 5438578787, 32631472723, 391577672677, 1566310690709, 50121942102689, 1503658263080671, 9021949578484027, 360877983139361081, 21652678988361664861, 476358937743956626943, 5716307252927479523317

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

Corresponding values of k are in A121799.

Sequence in context: A276665 A062573 A019435 * A084435 A072469 A004062

Adjacent sequences: A061089 A061090 A061091 * A061093 A061094 A061095

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