A111102 Cumulative sum of squares of Kolakoski sequence (A000002).

1, 5, 9, 10, 11, 15, 16, 20, 24, 25, 29, 33, 34, 35, 39, 40, 41, 45, 49, 50, 54, 55, 56, 60, 61, 65, 69, 70, 71, 75, 76, 77, 81, 82, 86, 90, 91, 95, 99, 100, 101, 105, 106, 110, 114, 115, 119, 120, 121, 125, 126, 127, 131, 135, 136, 140, 144, 145, 146, 150, 151, 155, 159, 160, 164, 168, 169, 170, 174

Offset

1,2

Comments

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.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{i=1..n} A000002(i)^2.

Mathematica

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 *)

Crossrefs

Cf. A000002.

Sequence in context: A268412 A043682 A335882 * A139456 A195684 A135980

Adjacent sequences: A111099 A111100 A111101 * A111103 A111104 A111105

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 13 2005

Status

approved