6 consecutive primes differ by 2n or more starting at a(n).

Terms

a(0) =3a(1) =73a(2) =523a(3) =683a(4) =13477a(5) =23087a(6) =47161a(7) =68281a(8) =68281a(9) =250501a(10) =250501a(11) =250501a(12) =1316041a(13) =1316041a(14) =2352289a(15) =8431127a(16) =8791801a(17) =8791801a(18) =8791801a(19) =8791801a(20) =14784911a(21) =14784911a(22) =14784911a(23) =14784911a(24) =107282507a(25) =107282507a(26) =107282507a(27) =554086993a(28) =554086993a(29) =554086993