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A172994 First number outperforming x=10 with simultaneous primality of {x^2k+x^k-1} for n values, starting with n=4, occurring with a smaller number than the n-th term of A096594. 0
2, 460724, 610357585, 2096681555 (list; graph; refs; listen; history; text; internal format)



This sequence is related to the remarkable occurrence of primes in the sequence 109, 10099, 1000999, etc. Credit for second and third terms goes to Jens Kruse Andersen.

Once a 5th term, a(8), is available, this sequence will be essentially complete: a(9)=66 and a(k)=2 for k>9 with near certainty (known true for several terms, and the contrary at any later point would 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).


Table of n, a(n) for n=4..7.


The first three terms are primes for all k from 1 through 4, 5 and 6; the fourth term is prime for k=1 to 6 and k=8, while x=10 requires k=9 to get the seventh prime.


Cf. A096594.

Sequence in context: A158346 A018854 A139181 * A214545 A072321 A237191

Adjacent sequences:  A172991 A172992 A172993 * A172995 A172996 A172997




James G. Merickel, Feb 07 2010



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Last modified April 17 09:05 EDT 2014. Contains 240634 sequences.