A051916 The Greek sequence: 2^a * 3^b * 5^c where a = 0,1,2,3,..., b,c in {0,1}, excluding the terms 1,2; that is: (a,b,c) != (0,0,0), (1,0,0).

3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1024, 1280, 1536, 1920, 2048, 2560, 3072, 3840, 4096, 5120, 6144, 7680, 8192, 10240, 12288, 15360, 16384, 20480

Offset

1,1

Comments

From Reinhard Zumkeller, Mar 19 2010: (Start)

Union of A007283, A020707, A020714, and A110286.

Intersection of A051037 and A003401 apart from terms 1 and 2. (End)

References

George E. Martin, Geometric Constructions, New York: Springer, 1997, p. 140.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2).

Formula

G.f.: x*(3*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 6*x^3 + 5*x^2 + 4*x + 3)/(1 - 2*x^4).

a(n+4) = 2*a(n) for n > 8. - Reinhard Zumkeller, Mar 19 2010

Sum_{n>=1} 1/a(n) = 17/10. - Amiram Eldar, Jan 18 2023

Mathematica

CoefficientList[Series[x(3x^7+2x^6+2x^5+2x^4+6x^3+5x^2+4x+3)/(1-2x^4), {x, 0, 60}], x] (* Harvey P. Dale, Dec 23 2012 *)

Prog

(PARI) Vec(x*(3*x^7+2*x^6+2*x^5+2*x^4+6*x^3+5*x^2+4*x+3)/(1-2*x^4)+O(x^99)) \\ Charles R Greathouse IV, Oct 12 2012

Crossrefs

Cf. A003401, A007283, A020707, A020714, A051037, A110286.

Sequence in context: A026506 A198382 A173946 * A130216 A120162 A002859

Adjacent sequences: A051913 A051914 A051915 * A051917 A051918 A051919

Keyword

nonn,easy,nice

Author

Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Dec 17 1999

Extensions

More terms from James A. Sellers, Dec 18 1999

Offset corrected by Reinhard Zumkeller, Mar 10 2010

Status

approved