[go: up one dir, main page]

login
A090773
Numbers that are congruent to {4, 6} mod 10.
4
4, 6, 14, 16, 24, 26, 34, 36, 44, 46, 54, 56, 64, 66, 74, 76, 84, 86, 94, 96, 104, 106, 114, 116, 124, 126, 134, 136, 144, 146, 154, 156, 164, 166, 174, 176, 184, 186, 194, 196, 204, 206, 214, 216, 224, 226, 234, 236, 244, 246, 254, 256, 264, 266, 274, 276, 284
OFFSET
1,1
FORMULA
a(n) = 2 * A047221(n) = 5*n-5/2-3*(-1)^n/2.
a(n) = 10*n-a(n-1)-10 (with a(1)=4). - Vincenzo Librandi, Nov 16 2010
G.f.: 2*x*(2+x+2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/10. - Amiram Eldar, Dec 28 2021
From Amiram Eldar, Nov 23 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = cosec(2*Pi/5) (A179290).
Product_{n>=1} (1 + (-1)^n/a(n)) = cosec(Pi/5)/2 (A300074). (End)
MATHEMATICA
#+{4, 6}&/@(10Range[0, 50])//Flatten (* or *) LinearRecurrence[{1, 1, -1}, {4, 6, 14}, 100] (* Harvey P. Dale, Jun 05 2017 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Giovanni Teofilatto, Feb 07 2004
EXTENSIONS
Edited and extended by Ray Chandler, Feb 10 2004
STATUS
approved