Primes 10k + 3 at the end of the maximal gaps in A269234.

Terms

a(0) =13a(1) =43a(2) =163a(3) =953a(4) =3163a(5) =4243a(6) =6473a(7) =8233a(8) =10093a(9) =13313a(10) =13463a(11) =27583a(12) =156253a(13) =1046833a(14) =1087423a(15) =4343873a(16) =5649433a(17) =9292193a(18) =18819653a(19) =32015773a(20) =38024653a(21) =53664593a(22) =90421003a(23) =133126013a(24) =169727903a(25) =228590863a(26) =284826133a(27) =318828313a(28) =431959873a(29) =949478653