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A034959 Divide even numbers into groups with prime(n) elements and add together.

%I A034959 #22 Mar 22 2023 21:59:47
%S A034959 2,18,70,182,484,884,1666,2546,4048,6612,8928,13172,17794,22274,28576,
%T A034959 37524,48380,57340,71556,85626,98550,118658,138112,163404,196134,
%U A034959 224220,249672,281838,310650,347136,420624,467670,525806,571846,655898
%N A034959 Divide even numbers into groups with prime(n) elements and add together.
%H A034959 Hieronymus Fischer, <a href="/A034959/b034959.txt">Table of n, a(n) for n = 1..10000</a>
%F A034959 From _Hieronymus Fischer_, Sep 27 2012: (Start)
%F A034959 a(n) = 2*Sum_{k=(A007504(n-1)+1)..A007504(n)} (k-1), n > 1.
%F A034959 a(n) = (A007504(n) - A007504(n-1))*(A007504(n) + A007504(n-1) - 1), n > 1.
%F A034959 a(n) = 2*(A000217(A007504(n) - 1) - A000217(A007504(n-1) - 1)), n > 1.
%F A034959 If we define A007504(0):=0, then the formulas above are also true for n=1.
%F A034959 a(n) = 2*A034957(n).
%F A034959 a(n) = A034960(n) - A000040(n).
%F A034959 (End)
%e A034959 {0,2} #2 S=2;
%e A034959 {4,6,8} #3 S=18;
%e A034959 {10,12,14,16,18} #5 S=70;
%e A034959 {20,22,24,26,28,30,32} #7 S=182.
%o A034959 (Python)
%o A034959 from itertools import islice
%o A034959 from sympy import nextprime
%o A034959 def A034959_gen(): # generator of terms
%o A034959     a, p = 0, 2
%o A034959     while True:
%o A034959         yield p*((a<<1)+p-1)
%o A034959         a, p = a+p, nextprime(p)
%o A034959 A034959_list = list(islice(A034959_gen(),20)) # _Chai Wah Wu_, Mar 22 2023
%Y A034959 Cf. A006003, A027441, A034960.
%Y A034959 Cf. A046992, A034956-A034958.
%K A034959 nonn
%O A034959 1,1
%A A034959 _Patrick De Geest_, Oct 15 1998