The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A034958 Divide primes into groups with prime(n) elements and add together. 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A049674 A077277 A073682 * A229008 A274322 A085350
KEYWORD
nonn
AUTHOR
Patrick De Geest, Oct 15 1998
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 12:18 EDT 2024. Contains 372630 sequences. (Running on oeis4.)