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.

2, 8, 7, 41, 42, 138, 143, 331, 348, 660, 864, 1444, 1322, 2349, 1824, 3195, 4122, 4696, 4264, 7184, 8038, 8259, 9988, 10972, 15151, 15446, 16954, 18322, 19994, 26001, 27985, 28426, 32541, 38963, 41797, 51790, 40074, 64140, 59403, 60066, 63732, 66980, 99172, 82152

Offset: 1

Author

Paolo Xausa, May 27 2021

Keywords

• nonn

Examples

			a(1) = 2 because the first subset is [1,2] (length = 2) and the sum of primes contained in it is 2.
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.
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.
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.
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000027, A000040, A007504, A034956, A344889.

Programs

Mathematica

nterms=50;list = TakeList[Range[Sum[Prime[i],{i,nterms}]],Prime[Range[nterms]]];Map[Total[Select[#,PrimeQ]]&,list]