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 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 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

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