A100585 a(n+1) = a(n)+floor(a(n)/3), a(1) = 3.

3, 4, 5, 6, 8, 10, 13, 17, 22, 29, 38, 50, 66, 88, 117, 156, 208, 277, 369, 492, 656, 874, 1165, 1553, 2070, 2760, 3680, 4906, 6541, 8721, 11628, 15504, 20672, 27562, 36749, 48998, 65330, 87106, 116141, 154854, 206472, 275296, 367061, 489414, 652552

Offset: 1

Author

N. J. A. Sloane, Dec 01 2004

Keywords

• nonn

Comments

Original definition: Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off every 4th term. Repeat, always crossing off every 4th term of those that remain. The numbers that are left form the sequence.

Can be stated as the number of animals starting from a single trio if any trio of animals can produce a single offspring. See A061418 for the equivalent sequence for pairs of animals. - Luca Khan, Sep 05 2024

Links

• Robert Israel, Table of n, a(n) for n = 1..7987
• Popular Computing (Calabasas, CA), Sieves: Problem 43, Vol. 2 (No. 13, Apr 1974), pp. 6-7. This is Sieve #6 with K=4. [Annotated and scanned copy]
• Index entries for sequences generated by sieves

Crossrefs

Cf. A003309, A003310, A100464, A100562, A003312, A003311, A052548, A100586, A061418.

Programs

Maple

R:= 3: x:= 3:
for i from 2 to 100 do x:= x + floor(x/3); R:= R,x od:
R; # Robert Israel, Sep 09 2024

Mathematica

t = Range[3, 2500000]; r = {}; While[Length[t] > 0, AppendTo[r, First[t]]; t = Drop[t, {1, -1, 4}];]; r (* Ray Chandler, Dec 02 2004 *)
NestList[#+Floor[#/3]&,3,50] (* Harvey P. Dale, Jan 14 2019 *)

PARI

a(n,s=3)=for(i=2,n,s+=s\3);s \\ M. F. Hasler, Oct 06 2014

Formula

a(1)=3, a(n+1) = a(n) + floor(a(n)/3). - Ben Paul Thurston, Jan 09 2008

Extensions

More terms from Ray Chandler, Dec 02 2004

Simpler definition from M. F. Hasler, Oct 06 2014