A109904 a(1) = 5. a(n+1) is the greatest prime of the form k*(a(n)-k) + 1. The least prime occurs for k = 1 and a(n+1) = a(n) in that case if no other value of k gives a prime then the sequence terminates.

5, 7, 13, 43, 463, 53593, 718052371, 128899801874680399, 4153789730832965126116749598699801, 4313492281993349218329412357362100514520987205269104143837429352069

Offset: 1

Author

Amarnath Murthy, Jul 15 2005

Keywords

• nonn

Comments

For the first five terms k = floor(a(n)/2). k can take values from 1 to floor(a(n)/2). It is conjectured that at least one value of k, 2 <= k < floor(a(n)/2) gives a prime and the sequence is infinite.

Examples

			a(2) = 2*3 + 1 = 7, a(3) = 3*4 + 1 = 13.
		

Links

• Jinyuan Wang, Table of n, a(n) for n = 1..13

Crossrefs

Cf. A026728, A109905.

Programs

PARI

{ b(n)=forstep(k=n\2,1,-1,if(isprime(k*(n-k)+1),return(k*(n-k)+1)));return(0) }
s=5;while(1,print1(s, ", ");s=b(s)) \\ Max Alekseyev, Oct 04 2005

Extensions

More terms from Max Alekseyev, Oct 04 2005