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%I #8 Jul 17 2021 11:21:25
%S 360,120,24,17,2,9,4,64,3,6,1,72,102,119,66,51,34,66,89,283,52,84,59,
%T 554,81,44,328,69,26,36,101,42,898,17,121,193,69,137,346,2,868,412,
%U 101,247,417,1732,206,2278,109,762,87,268,511,1213,108,41,43,946,483,706,72
%N Least k such that k*prime(n)#/5 - 5 and k*prime(n)#/5 + 5 are consecutive primes with gap 10, where prime(n)# is the n-th primorial.
%e 360*2/5=144, 139 and 149 are consecutive primes with gap 10, so a(1) = 360.
%e 120*2*3/5=144, so a(2) = 120.
%e 24*2*3*5/5=144, so a(3) = 24.
%e 17*2*3*5*7/5=714, 709 and 719 are consecutive primes with gap 10, so a(4) = 17.
%t a[n_] := Module[{k = 1, p = Product[Prime[i], {i,1,n}]}, While[!(PrimeQ[k*p/5-5] && NextPrime[k*p/5-5] == k*p/5+5), k++]; k]; Array[a, 60] (* _Amiram Eldar_, Jul 17 2021 *)
%Y Cf. A002110.
%Y Cf. A097439, A097440, A097441, A098064.
%K nonn
%O 1,1
%A _Pierre CAMI_, Aug 28 2004
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