A182664 a(n) = A088828(n) + A157502(n).
5, 11, 15, 21, 25, 29, 35, 39, 43, 47, 53, 57, 61, 65, 69, 75, 79, 83, 87, 91, 95, 101, 105, 109, 113, 117, 121, 125, 131, 135, 139, 143, 147, 151, 155, 159, 165, 169, 173, 177, 181, 185, 189, 193, 197, 203, 207, 211, 215, 219, 223, 227, 231, 235, 239, 245
Offset: 1
Keywords
Programs
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Mathematica
Module[{nn=60,tb},tb=2*Accumulate[Table[If[IntegerQ[(Sqrt[8n+1]-1)/2],1,0],{n,nn}]];Join[{5},Table[1+4i+tb[[i-1]],{i,2,nn}]]] (* Harvey P. Dale, Jul 22 2013 *)
Formula
Let T(n) be 1 if positive n is a triangular number, else 0; we also define T(0) as 0. Then we can also write this sequence as 1 + 4*n + 2*[T(1) + T(2) ... T(n-1)]. (Other than the special definition for T(0), T(n) is essentially A010054.)
The sequence can also be seen visually as
1 + 4
1 + 4 + 6
1 + 4 + 6 + 4
1 + 4 + 6 + 4 + 4
1 + 4 + 6 + 4 + 4 + 6
1 + 4 + 6 + 4 + 4 + 6 + 4
1 + 4 + 6 + 4 + 4 + 6 + 4 + 4
1 + 4 + 6 + 4 + 4 + 6 + 4 + 4 + 4
1 + 4 + 6 + 4 + 4 + 6 + 4 + 4 + 4 + 6...