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A344718 Divide the positive integers into subsets of lengths given by successive primes. a(n) is the sum of primes contained in the n-th subset.

%I A344718 #18 Sep 05 2023 12:22:12
%S A344718 2,8,7,41,42,138,143,331,348,660,864,1444,1322,2349,1824,3195,4122,
%T A344718 4696,4264,7184,8038,8259,9988,10972,15151,15446,16954,18322,19994,
%U A344718 26001,27985,28426,32541,38963,41797,51790,40074,64140,59403,60066,63732,66980,99172,82152
%N A344718 Divide the positive integers into subsets of lengths given by successive primes. a(n) is the sum of primes contained in the n-th subset.
%H A344718 Paolo Xausa, <a href="/A344718/b344718.txt">Table of n, a(n) for n = 1..1000</a>
%e A344718 a(1) = 2 because the first subset is [1,2] (length = 2) and the sum of primes contained in it is 2.
%e A344718 a(2) = 8 because the second subset is [3,4,5] (length = 3) and the sum of primes contained in it is 3 + 5 = 8.
%e A344718 a(3) = 7 because the third subset is [6,7,8,9,10] (length = 5) and the sum of primes contained in it is 7.
%e A344718 a(4) = 41 because the fourth subset is [11,12,13,14,15,16,17] (length = 7) and the sum of primes contained in it is 11 + 13 + 17 = 41.
%t A344718 nterms=50;list = TakeList[Range[Sum[Prime[i],{i,nterms}]],Prime[Range[nterms]]];Map[Total[Select[#,PrimeQ]]&,list]
%Y A344718 Cf. A000027, A000040, A007504, A034956, A344889.
%K A344718 nonn
%O A344718 1,1
%A A344718 _Paolo Xausa_, May 27 2021