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

1,1

Links

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

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)

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A006003, A027441, A034956.

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

Sequence in context: A049674 A077277 A073682 * A229008 A274322 A085350

Adjacent sequences: A034955 A034956 A034957 * A034959 A034960 A034961

Keyword

nonn

Author

Patrick De Geest, Oct 15 1998

Status

approved