A153089 Continue with summing & priming the A013918 list.

2, 7, 117241, 1351781, 3703429, 243729623, 486707171, 568561471, 766634423, 883314979, 1058403331, 1520509423, 1933700891, 1997566367, 2063533819, 2632011079, 3040681037, 3591772153, 4114380107, 7870826569, 8414671219

Offset: 1

Author

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

Keywords

• nonn

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

Crossrefs

Cf. A000040, A013918.

Programs

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