OFFSET
1,1
COMMENTS
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[].
LINKS
M. J. Crowe, Table of n, a(n) for n = 1..10000
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael J. Crowe (michaelcrowe117(AT)btinternet.com), Dec 18 2008
STATUS
approved