A096100 a(1) = 1; for n > 1: a(n) = smallest number >1 such that product of any two or more successive terms + 1 is prime.

1, 2, 2, 3, 6, 46, 1306, 7695, 17383720, 2183805400, 60512359083, 447808566362, 181830203704703

Offset: 1

Author

Amarnath Murthy, Jun 24 2004

Keywords

• more
• nonn

Comments

a(14) > 2.5*10^14, if it exists. - Don Reble, Nov 22 2015

So far, up through a(13), the sequence is nondecreasing. I don't know a good reason why it should stay that way. (But since candidates for each successive value get rarer, the least candidate will tend to increase.) - Don Reble, Nov 22 2015

I don't think it will be easy to prove that this sequence is nondecreasing. The analogous sequence with other starting values often leads to non-monotonic sequences, e.g., (3, 2, 2, 3, 26, 876, 15136, ...), (4, 3, 6, 6, 5, 14, 3597, 1218704, ...), or (5, 2, 3, 2, 3, 1176, 40, 142863, ...). - M. F. Hasler, Nov 24 2015

Examples

			a(4) is not 2 since 2*2*2 + 1 = 9 is composite, but 2*3 + 1 = 7, 2*2*3 + 1 = 13, 1*2*2*3 + 1 = 13 are all prime, hence a(4) = 3.
		

Programs

PARI

A096100(n, show=0, a=[1])={for(n=1, n-1, show&&print1(a[n]", "); for(k=2, 9e9, my(p=1); for(i=0,n-1,isprime(1+k*p*=a[n-i])||next(2)); a=concat(a,k); break)); a[n]} \\ Use 2nd or 3rd optional arg to print intermediate terms or to use other starting value(s) of the sequence. Not efficient enough to go beyond a(8). - M. F. Hasler, Nov 24 2015

Extensions

Edited, corrected and extended by Klaus Brockhaus, Jul 05 2004

a(10) from Donovan Johnson, Apr 22 2008

a(11)-a(13) from Don Reble, Nov 22 2015