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a(n) is the smallest positive d such that the n-th prime is the smallest prime p for which p+d is also prime.
6

%I #8 Nov 16 2019 03:50:14

%S 1,2,6,22,116,88,470,112,284,242,202,772,1326,718,1334,1328,2558,1762,

%T 1642,2402,3274,1732,7094,9512,7984,5246,12688,10532,9952,16766,7702,

%U 60458,9974,25708,5888,13528,10342,25678,62156,69518,76838,37666

%N a(n) is the smallest positive d such that the n-th prime is the smallest prime p for which p+d is also prime.

%C Except for n=1, A020483(a(n)/2) is the first appearance of the n-th prime. It is conjectured that a(n) always exists. a(386) is the first number which must be above 10^12.

%H J. K. Andersen, <a href="http://groups.yahoo.com/group/primenumbers/message/15641">Prime gaps (not necessarily consecutive)</a>.

%H Mike Oakes, Ed Pegg Jr, Jens Kruse Andersen, <a href="/A101042/a101042.txt">Prime gaps (not necessarily consecutive)</a>, digest of 5 messages in primenumbers Yahoo group, Nov 26 - Nov 27, 2004. [Cached copy]

%e a(3)=6 because: The 3rd prime is 5. 2+6, 3+6 is composite, 5+6 is prime. 6 is the smallest such number.

%Y Cf. A020483, A101043, A101044, A101045, A101046.

%K nonn

%O 1,2

%A _Jens Kruse Andersen_, Nov 28 2004