%I A079900
%S A079900 1,1,1,1,1,2,1,2,1,1,5,3,4,2,3,7,21,9,3,34,32,5,7,16,8,4,2,28,21,7,203,
%T A079900 100,28,15,126,14,63,35,253,520,910,105,264,665,1155,165,504,1155,858,
%U A079900 156,495,91,539,715,198,507,550,275,143,720,627,2002,2618,5695,4692
%N A079900 a(n) = the smallest positive number which furnishes a "one-line proof" 
               for primality of prime(n), the n-th prime; i.e. the smallest k which 
               is relatively prime to p such that k*(p+k) is divisible by every 
               prime less than sqrt(p), where p=prime(n).
%C A079900 A one-line proof looks like this: 101 = 2*3*3*7 - 5*5. For each prime 
               Q up to the square-root of p(n), either the left product or the right 
               product is divisible by Q, but not both. It follows that the difference 
               is not divisible by any such Q and so is prime. The sequence gives 
               the right (smaller) number.
%C A079900 The idea comes from seqfan postings by Don McDonald and David W. Wilson.
%D A079900 R. K. Guy, Lacampagne and J. Selfridge, Primes at a glance, Math Comput 
               48(1987) 183-202; Math. Rev. 87m:11008.
%e A079900 a(6)=2: The 6-th prime is 13 and the equation 13 = 3*5 - 2 proves it.
%t A079900 a[p_] := Module[{prod, k}, prod=Times@@Prime/@Range[PrimePi[Sqrt[p]]]; 
               For[k=1, True, k++, If[GCD[p, k]==1&&Mod[k*(p+k), prod]==0, Return[a[p]=k]]]]; 
               a/@Prime/@Range[70]
%Y A079900 Sequence in context: A083531 A003417 A158986 this_sequence A117354 A140324 
               A010250
%Y A079900 Adjacent sequences: A079897 A079898 A079899 this_sequence A079901 A079902 
               A079903
%K A079900 nonn
%O A079900 1,6
%A A079900 Don Reble (djr(AT)nk.ca), Feb 20 2003
%E A079900 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Feb 24 2003