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%I #13 Dec 30 2019 13:27:14
%S 1,5,9,10,11,15,16,20,24,25,29,33,34,35,39,40,41,45,49,50,54,55,56,60,
%T 61,65,69,70,71,75,76,77,81,82,86,90,91,95,99,100,101,105,106,110,114,
%U 115,119,120,121,125,126,127,131,135,136,140,144,145,146,150,151,155,159,160,164,168,169,170,174
%N Cumulative sum of squares of Kolakoski sequence (A000002).
%C a(n) is prime for n = 2, 5, 11, 17, 25, 29. a(n) is semiprime for n = 3, 4, 6, 10, 12, 13, 14, 15, 19, 22, 26, 27. a(n) is a perfect square for n = 1, 3, 7, 10, 19.
%H G. C. Greubel, <a href="/A111102/b111102.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{i=1..n} A000002(i)^2.
%t A000002[n_]:= If[n<3, Max[0, n], Module[{an = {1,2,2}, m = 3}, While[Length[an] < n, an = Join[an, Table[Mod[m, 2, 1], {an[[m]]}]]; m++]; an[[n]]]]; Table[Sum[A000002[j]^2, {j, n}], {n, 1, 70}] (* _G. C. Greubel_, Dec 18 2019; Somos code of A000002 *)
%Y Cf. A000002.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Oct 13 2005