1,1

If level 1 sum primes is the prime number list A000040.

and level 2 sum primes is the list A013918 then the above list is level 3.

Continue with summing & priming for Level 4 sum primes which are

2, 50575480511, 158413287841, 379787123171, 88082548147771,

3939163325960453, 4342203121792903, 41672041797268133, 92013021551247323,

145937058697288751, 157891295660264779, 270930872865589619,...

Again continue with summing & priming for Level 5 sum primes which are

2, 50575480513, 1663807730918617976723, 14304824932873646803553,

28817336920092499216069, 20284632396728311969809131,

168804229342169123733371839,909257309497199880752121319,...

Again continue with summing & priming for Level 6 sum primes which are

2, @Prime[1]

22388562459746799685433396747, @Prime[57000046]

????

Initially found using Mathematica then a NTL+C program using Miller-witness

10 trials.Checked summed primes with PrimeQ[].

M. J. Crowe, Table of n, a(n) for n=1,...,10000

lst2={}; s2=0; Do[s2=s2+Prime[n]; If[PrimeQ[s2], AppendTo[lst2, s2]], {n, 4700}]; lst3={}; s3=0; Do[s3=s3+lst2[[n]]; If[PrimeQ[s3], AppendTo[lst3, s3]], {n, 1, Length[lst2]}]; lst3

Cf. A000040, A013918

Sequence in context: A138198 A106023 A152181 this_sequence A077548 A050809 A095217

Adjacent sequences: A153086 A153087 A153088 this_sequence A153090 A153091 A153092

nonn

Michael J. Crowe (michaelcrowe117(AT)btinternet.com), Dec 18 2008