Most "compact" sequence such that there is at least one prime between a(n) and a(n+1)

[Maximilian Hasler]

in fact the prime gap following  A002386[68] is 1248=A005250[69]
which indicates that  A002386[68] should be the 69-th element of that
sequence, and the term A002386[68] is missing.

gp > vector(# A002386,i,nextprime( A002386[i]+1)- A002386[i])
%227 = [1, 2, 4, 6, 8, 14, 18, 20, 22, 34, 36, 44, 52, 72, 86, 96,
112, 114, 118, 132, 148, 154, 180, 210, 220, 222, 234, 248, 250, 282,
288, 292, 320, 336, 354, 382, 384, 394, 456, 464, 468, 474, 486, 490,
500, 514, 516, 532, 534, 540, 582, 588, 602, 652, 674, 716, 766, 778,
804, 806, 906, 916, 924, 1132, 1184, 1198, 1220, 1248]

in http://www.research.att.com/~njas/sequences/b000101.txt we find
68 203986478517457213

thus,
gp > precprime(203986478517457213-1)
%228 = 203986478517455989

should be the correct value of A002386[68]

M.H.