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Least number, k which is a multiple of a primorial, such that p-n*k, p-(n-1)k, p-(n-2)k, ... p-2k, p-k, p, p+k, p+2k, ... p+(n-2)k, p+(n-1)k and p+n*k are all prime with p being the k-th prime.
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%I #3 Mar 30 2012 17:31:17

%S 2,6,720,252420,2053380

%N Least number, k which is a multiple of a primorial, such that p-n*k, p-(n-1)k, p-(n-2)k, ... p-2k, p-k, p, p+k, p+2k, ... p+(n-2)k, p+(n-1)k and p+n*k are all prime with p being the k-th prime.

%e a(1)=2 which is a multiple of a primorial.

%e a(2)=6 because p=13 and p-6=7 & p+6=19 all of which are prime and 6 is of the form 2*3*m, A002110.

%e a(3)=720 because p=5443 and p-720=4723, p-2*720=4003, p+720=6163 & p+2*720=6883 all of which are prime and 720 is of the form 2*3*5*m.

%e a(4)=252420 because p

%t f[n_] := Block[{p = Fold[Times, 1, Prime[ Range[ n]]]},

%Y Cf. A064403, A112530.

%K hard,nonn

%O 1,1

%A _Robert G. Wilson v_, Sep 10 2005