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%I #7 Jul 17 2021 11:21:43
%S 1,2,7,6,6,104,152,116,181,6,78,89,85,262,133,57,77,35,237,140,315,
%T 397,663,48,1135,382,318,261,542,352,120,31,1430,553,43,913,1235,122,
%U 1008,602,222,1562,255,6293,1231,2507,1029,1413,5986,3860,45,2622,3033,457
%N Least k such that k*((prime(n)#)^2)-1 and k*((prime(n)#)^2)+1 are twin primes.
%e 1*((2*3)^2)-1 = 35 is composite, 2*((2*3)^2)-1 = 71 is prime, 2*((2*3)^2)+1 = 73 is prime twin of 71 so a(2) = 2.
%t a[n_] := Module[{k = 1, p = Product[Prime[i], {i,1,n}]}, While[!(PrimeQ[k*p^2-1] && NextPrime[k*p^2-1] == k*p^2+1), k++]; k]; Array[a, 50] (* _Amiram Eldar_, Jul 17 2021 *)
%Y Cf. A001097, A002110.
%K nonn
%O 1,2
%A _Pierre CAMI_, Mar 23 2005
%E More terms from _Amiram Eldar_, Jul 17 2021
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