cp's OEIS Frontend

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).

%I A051916 #35 Jul 02 2025 16:01:58
%S A051916 3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,128,160,192,
%T A051916 240,256,320,384,480,512,640,768,960,1024,1280,1536,1920,2048,2560,
%U A051916 3072,3840,4096,5120,6144,7680,8192,10240,12288,15360,16384,20480
%N 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).
%C A051916 From _Reinhard Zumkeller_, Mar 19 2010: (Start)
%C A051916 Union of A007283, A020707, A020714, and A110286.
%C A051916 Intersection of A051037 and A003401 apart from terms 1 and 2. (End)
%D A051916 George E. Martin, Geometric Constructions, New York: Springer, 1997, p. 140.
%H A051916 Reinhard Zumkeller, <a href="/A051916/b051916.txt">Table of n, a(n) for n = 1..1000</a>
%H A051916 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2).
%F A051916 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).
%F A051916 a(n+4) = 2*a(n) for n > 8. - _Reinhard Zumkeller_, Mar 19 2010
%F A051916 Sum_{n>=1} 1/a(n) = 17/10. - _Amiram Eldar_, Jan 18 2023
%t A051916 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 *)
%o A051916 (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
%o A051916 (Python)
%o A051916 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
%Y A051916 Cf. A003401, A007283, A020707, A020714, A051037, A110286.
%K A051916 nonn,easy,nice
%O A051916 1,1
%A A051916 Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr), Dec 17 1999
%E A051916 More terms from _James Sellers_, Dec 18 1999
%E A051916 Offset corrected by _Reinhard Zumkeller_, Mar 10 2010