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%I #9 Oct 26 2019 02:05:42
%S 3,13,31,89,181,661,113,2113,523,13421,2311,4177,35543,39901,4831,
%T 44417,1327,12853,119321,52321,82657,36389,136897,203713,95651,59281,
%U 255259,178697,531919,427621,2640581,1414849,643303,3021173,175141
%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.
%e a(49) = 604073 because gcd(604073-1, 604171-1) = gcd(6164*98, 6165*98) = 98 = 2n.
%e a(4) = 89 because gcd(89-1, 97-1) = gcd(8*11, 8*16) = 8 = 2n and these primes are the smallest with this property.
%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}]; a
%t With[{tsp={#[[1]],#[[2]],GCD[#[[1]]-1,#[[2]]-1]}&/@Partition[Prime[ Range[ 300000]],2,1]}, Transpose[Flatten[Table[Select[tsp, Last[#]==2n&,1],{n,40}],1]][[1]]] (* _Harvey P. Dale_, Jul 07 2013 *)
%Y Cf. A006093, A067605.
%K nonn
%O 1,1
%A _Labos Elemer_, Dec 06 2000
%E Edited by _Robert G. Wilson v_, Feb 01 2002
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