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a(n) is the smallest odd prime p that has exactly n consecutive distinct prime "prime gaps" between p and a larger prime.
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%I #19 Mar 19 2018 06:40:03

%S 7,19,79,491,2153,8123,8123,66137,749467,24935909,128200879,128200883,

%T 7256916503,61070523827,181066533587,1940791472069,12233504578289,

%U 274988895429719

%N a(n) is the smallest odd prime p that has exactly n consecutive distinct prime "prime gaps" between p and a larger prime.

%C Here, prime gap is defined as the number of composites between a prime and the next prime.

%H Caldwell and Honaker, <a href="https://primes.utm.edu/curios/page.php?number_id=16869">Prime Curios!</a>

%e a(4) = 491 because 491 (followed by 7 composites) 499 (followed by 3 composites) 503 (followed by 5 composites) 509 (followed by 11 composites) 521, and {7, 3, 5, 11} are 4 consecutive distinct prime prime gaps.

%Y Cf. A000040, A065091.

%K nonn,more

%O 1,1

%A _G. L. Honaker, Jr._, Mar 09 2018

%E a(5)-a(12) from Chuck Gaydos

%E a(13)-a(18) from _Giovanni Resta_, Mar 19 2018