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

Author

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

Keywords

• nonn
• easy
• nice

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).

Crossrefs

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

Programs

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 *)

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

Python

def A051916(n): return n+2 if n<5 else (15,1,5,3)[m:=n&3]<<(n>>2)+(-2,2,0,1)[m] # Chai Wah Wu, Apr 02 2025

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

Extensions

More terms from James Sellers, Dec 18 1999

Offset corrected by Reinhard Zumkeller, Mar 10 2010