n(k) is the minimum number that require at least k to make Prime[n]+2*Prime[n+k] a prime.

Terms

a(0) =2a(1) =10a(2) =9a(3) =7a(4) =8a(5) =40a(6) =80a(7) =28a(8) =34a(9) =73a(10) =52a(11) =174a(12) =86a(13) =105a(14) =127a(15) =161a(16) =326a(17) =225a(18) =356a(19) =154a(20) =245a(21) =394a(22) =362a(23) =350a(24) =279a(25) =586a(26) =846a(27) =321a(28) =929a(29) =1822