Search: id:A072664
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%I A072664
%S A072664 2,7,107,2187,578309,12239309,45640671719
%N A072664 End of smallest run of n consecutive integers with n, n-1, ..., 1 distinct 
               prime factors in that order.
%C A072664 Using a musical analogy, each run is a "crescendo" of primality where 
               each subsequent member of the run is gradually "more prime" in the 
               sense of having one fewer distinct prime factors (see A001221). These 
               a(n) are the peaks of crescendos of increasing length. a(7) is greater 
               than 60000000.
%C A072664 This sequence and A072663 were inspired by A068069, where the members 
               of the runs have n different numbers of distinct prime factors, 1 
               through n, but where the order is not specified.
%e A072664 a(1)=2 because 2 is prime and therefore the smallest integer with exactly 
               one distinct prime factor. a(2)=7 because 6=2*3 and 7 (prime) is 
               the smallest run of consecutive integers with exactly 2 and 1 distinct 
               prime factors in that order. a(3)=107 because 105=3*5*7, 106=2*53 
               and 107 (prime) is the smallest run with exactly 3, 2 and 1 distinct 
               prime factors in that order. Note that a(1), a(2), a(3), a(5) and 
               a(6) are prime but that a(4)=2187=3^7 is not.
%Y A072664 Cf. A072663 (smallest start with run pattern 1, 2, ..., n), A072665 (center 
               with run pattern n+1, n, ..., 2, 1, 2, ..., n, n+1), A068069 (run 
               order not specified), A001221 (omega(n)).
%Y A072664 Sequence in context: A102747 A122524 A162634 this_sequence A045310 A000157 
               A034902
%Y A072664 Adjacent sequences: A072661 A072662 A072663 this_sequence A072665 A072666 
               A072667
%K A072664 nonn
%O A072664 1,1
%A A072664 Rick L. Shepherd (rshepherd2(AT)hotmail.com), Jun 30 2002
%E A072664 a(7) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jan 24 2009

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