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

1,1

Links

Table of n, a(n) for n=1..56.

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...

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 *)

Crossrefs

Cf. A088828 and A157502. Also alternate generation formula related to A000217, A010054.

Sequence in context: A314037 A224213 A036787 * A299976 A187715 A314038

Adjacent sequences: A182661 A182662 A182663 * A182665 A182666 A182667

Keyword

nonn

Author

Ed Smiley, Dec 23 2012

Status

approved