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A182664 a(n) = A088828(n) + A157502(n). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 12 11:51 EDT 2021. Contains 342920 sequences. (Running on oeis4.)