A130216 a(0) = 3; a(n) = a(n-1) + (number of multiples of 3 so far in the sequence).

3, 4, 5, 6, 8, 10, 12, 15, 19, 23, 27, 32, 37, 42, 48, 55, 62, 69, 77, 85, 93, 102, 112, 122, 132, 143, 154, 165, 177, 190, 203, 216, 230, 244, 258, 273, 289, 305, 321, 338, 355, 372, 390, 409, 428, 447, 467, 487, 507, 528, 550, 572, 594, 617, 640, 663, 687, 712

Offset

0,1

Comments

See A007980 for the same construction with multiples of 2.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: -(3*x^8-2*x^7+x^4-2*x+3) / (x^9-2*x^8+x^7-x^2+2*x-1). - Alois P. Heinz, Aug 12 2009

Example

3,4,5,6,8,10,12,15: next term is 19 which is 15 + 4 previous terms divisible by 3 (they are 3,6,12,15).

Maple

a:= proc(n) local m, r; m:= iquo(n, 7, 'r'); (3+21*m+6*r) *m/2 +[3, 4, 5, 6, 8, 10, 12][r+1] end: seq(a(n), n=0..80); # Alois P. Heinz, Aug 12 2009

Mathematica

l={3}; Do[AppendTo[l, Last[l]+Count[l, _?(Divisible[#, 3]&)]], {n, 60}]; l (* Harvey P. Dale, Jul 24 2011 *)

Crossrefs

Sequence in context: A198382 A173946 A051916 * A120162 A002859 A180646

Adjacent sequences: A130213 A130214 A130215 * A130217 A130218 A130219

Keyword

easy,nonn

Author

Eric Angelini, Aug 05 2007

Extensions

More terms from Alois P. Heinz, Aug 12 2009

Status

approved