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Least k such that k*prime(n)#/6 - 6 and k*prime(n)#/6 + 6 are consecutive primes with gap of 12 for n > 2.
4

%I #8 Jul 17 2021 11:21:31

%S 41,43,19,25,29,119,35,73,83,337,193,71,137,7,515,731,53,211,353,247,

%T 1415,65,223,77,481,191,331,367,605,769,77,1751,221,617,713,683,1325,

%U 233,187,259,641,235,545,2761,1993,71,851,527,1159,757,239,1817,3203

%N Least k such that k*prime(n)#/6 - 6 and k*prime(n)#/6 + 6 are consecutive primes with gap of 12 for n > 2.

%e 43*prime(4)#/6-6 = 43*2*3*5*7/6-6 = 1499, 43*prime(4)#/6+6 = 43*2*3*5*7/6+6 = 1511, 1499 and 1511 are consecutive primes with gap of 12, so a(4) = 43.

%t a[n_] := Module[{k = 1, p = Product[Prime[i], {i,1,n}]}, While[!(PrimeQ[k*p/6-6] && NextPrime[k*p/6-6] == k*p/6+6), k++]; k]; Array[a, 60, 3] (* _Amiram Eldar_, Jul 17 2021 *)

%Y Cf. A002110.

%Y Cf. A097439, A097440, A097441, A097570.

%K nonn

%O 3,1

%A _Pierre CAMI_, Sep 11 2004