A172994 a(n), starting at n=4, is the smallest positive integral x with an n-th prime in {x^2k+x^k-1} occurring for k < A096594(n).

2, 460724, 610357585, 2096681555, 5351622936, 66, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 4

Author

James G. Merickel, Feb 07 2010

Keywords

• more
• nonn

Comments

Note that the offset here is 4 for the reason that 10^2k+10^k-1 is prime for k=1 through 3 but not for k=4. This sequence is related to the remarkable occurrence of primes in the sequence 109, 10099, 1000999, etc. Second and third terms from Jens Kruse Andersen (prior to submission).

This sequence is essentially complete: a(k)=2 for k>9 with near certainty. That is, assuming the referenced sequences being compared are correct (and they have been checked), this is absolutely known true through a(25); and the contrary at any later point would be comparable to a return to the origin of a random walk on the line that is biased in one direction and already many 'paces' along in that direction. - James G. Merickel, Apr 16 2014

Examples

			a(9)=66 corresponds to the fact that 66^48+66^24-1 is already the 9th prime value of type x^2k+x^k-1 for x=66 (i.e., this surpasses A096594(9)=26, that 10^52+10^26-1 is the 9th prime for the case x=10).
		

Crossrefs

Cf. A096594, A098855.

Extensions

a(9)-a(28) added by James G. Merickel, Mar 23 2014