A034958 Divide primes into groups with prime(n) elements and add together.

5, 23, 101, 311, 931, 1895, 3875, 6349, 10643, 18335, 25873, 39593, 55607, 71301, 94559, 127315, 167495, 204063, 258283, 315087, 369749, 451635, 533015, 640097, 779283, 902789, 1013795, 1159073, 1295871, 1457935, 1786691, 2002645, 2272221

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn

Examples

			a(1) = 5 because the first 2 primes are 2 and 3 and 2 + 3 = 5.
a(2) = 23 because the next 3 primes are 5, 7, 11, and they add up to 23.
a(3) = 101 because the next 5 primes are 13, 17, 19, 23, 29 which add up to 101.
a(4) = 311 because the next 7 primes are 31, 37, 41, 43, 47, 53, 59 and they add up to 311.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006003, A027441, A034956.

Cf. A007504, A046992, A034959, A034960, A180302.

Programs

Mathematica

Join[{5},Total[Prime[Range[#[[1]]+1,#[[2]]]]]&/@Partition[ Accumulate[ Prime[ Range[40]]],2,1]] (* Harvey P. Dale, Oct 03 2013 *)
Module[{nn=33},Total/@TakeList[Prime[Range[Total[Prime[Range[nn]]]]], Prime[ Range[ nn]]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Mar 16 2018 *)
s = 0; Total[Table[s = s + 1; Prime[s], {j, 33}, {n, Prime[j]}], {2}] (* Horst H. Manninger, Jan 17 2019 *)

PARI

s(n) = sum(k=1, n, prime(k)); \\ A007504
a(n) = s(s(n)) - s(s(n-1)); \\ Michel Marcus, Oct 12 2018

Formula

From Hieronymus Fischer, Sep 26 2012: (Start)

a(n) = Sum_{k=A007504(n-1)+1..A007504(n)} A000040(k), n > 1.

a(n) = A007504(A007504(n)) - A007504(A007504(n-1)), n > 1.

If we define A007504(0) := 0, then the formulas are also true for n = 1.

(End)