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 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). 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 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 LINKS EXAMPLE 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. Sequence in context: A158346 A018854 A139181 * A214545 A072321 A237191 Adjacent sequences:  A172991 A172992 A172993 * A172995 A172996 A172997 KEYWORD more,nonn AUTHOR James G. Merickel, Feb 07 2010 EXTENSIONS a(9)-a(28) added by James G. Merickel, Mar 23 2014 STATUS approved

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