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%I #10 Oct 18 2019 03:59:42
%S 3,7,23,359,139,467,293,3391,1259,17519,3739,7079,12011,52639,18869,
%T 66239,77383,27143,51071,76039,119447,76163,91033,226943,206699,
%U 894451,327347,492911,399793,195599,313409,981823,829883,1169939,302329
%N Smallest prime p of two consecutive primes, p < q, such that gcd(p+1, q+1) = 2n.
%C Since all consecutive primes, p < q and p greater than 2, are odd, therefore gcd(p+1, q+1) must be even.
%H Charles R Greathouse IV, <a href="/A067604/b067604.txt">Table of n, a(n) for n = 1..200</a>
%e a(1) = 3, the 3rd prime being the first entry in A066940;
%e a(2) = 7, the 4th prime being the first entry in A066941;
%e a(3) = 23, the 9th prime being of the first entry in A066942;
%e a(4) = 359, the 72nd prime being the first entry in A066943;
%e a(5) = 139, the 34th prime being the first entry in A066944.
%t a = Table[0, {100}]; p = 3; q = 5; Do[q = Prime[n + 1]; d = GCD[p + 1, q + 1]/2; If[d < 101 && a[[d]] == 0, a[[d]] = n]; b = c, {n, 2, 10^7}]; Prime[a]
%o (PARI) a(n)=my(k=2*n); forstep(p=k-1,oo,k, if(isprime(p) && (nextprime(p+1)-p)%k==0, return(p))) \\ _Charles R Greathouse IV_, Aug 17 2015
%Y Cf. A066940, A066941, A066942, A066944, A067603.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 31 2002
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