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%I #14 Oct 12 2022 11:45:36
%S 2,7,31,71,59,331,569,263,691,977,1091,2089,1487,2417,2797,10223,4987,
%T 6427,12743,9811,17041,29423,12739,20323,20147,17839,53017,53693,
%U 17033,67261,151169,106357,129517,185153,77969,253609,185477,140717
%N a(n) is the least prime p, such that next_prime(2*p) - 2*p = 2*n - 1.
%C Previous name was: Smallest p primes which give q=2p+2n-1 primes. Smallest Sophie Germain primes generalized in a possible way: 1 is replaced by 2n-1.
%F Min{p|p and q=2p+2n-1 are primes}.
%e For n=1,2,3,4, 2n-1=1,3,5,7 and 2*{2,7,31,71,...} + {1,3,5,7,...} = {5,17,67,149,...}. For n=75, a(75)=140717 a prime gives 2*140717 + 75 = 281509, a new prime.
%t Array[(k = 1; While[NextPrime[2 #2] - 2 #2 != #1 & @@ {#, Prime[k]}, k++]; Prime[k]) &[2 # - 1] &, 38] (* _Michael De Vlieger_, Oct 12 2022 *)
%Y Cf. A005384, A005385, A059847.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 26 2001
%E Offset corrected by _Sean A. Irvine_, Oct 12 2022
%E New name from _Sean A. Irvine_, Oct 12 2022
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