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%I #39 May 15 2014 10:03:07
%S 2,460724,610357585,2096681555,5351622936,66,2,2,2,2,2,2,2,2,2,2,2,2,
%T 2,2,2,2,2,2,2
%N 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).
%C 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).
%C 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
%e 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).
%Y Cf. A096594, A098855.
%K more,nonn
%O 4,1
%A _James G. Merickel_, Feb 07 2010
%E a(9)-a(28) added by _James G. Merickel_, Mar 23 2014
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