|
%I #52 Sep 08 2022 08:44:42
%S 6,15,24,33,42,51,60,69,78,87,96,105,114,123,132,141,150,159,168,177,
%T 186,195,204,213,222,231,240,249,258,267,276,285,294,303,312,321,330,
%U 339,348,357,366,375,384,393,402,411,420,429,438,447,456,465,474,483
%N a(n) = 9*n + 6.
%C General form: (q*n-1)*q, cf. A017233 (q=3), A098502 (q=4). - _Vladimir Joseph Stephan Orlovsky_, Feb 16 2009
%C Numbers whose digital root is 6; that is, A010888(a(n)) = 6. (Ball essentially says that Iamblichus (circa 350) announced that a number equal to the sum of three integers 3n, 3n - 1, and 3n - 2 has 6 as what is now called the number's digital root.) - _Rick L. Shepherd_, Apr 01 2014
%D W. W. R. Ball, A Short Account of the History of Mathematics, Sterling Publishing Company, Inc., 2001 (Facsimile Edition) [orig. pub. 1912], pages 110-111.
%H Vincenzo Librandi, <a href="/A017233/b017233.txt">Table of n, a(n) for n = 0..5000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: 3*(2+x)/(x-1)^2 . - _R. J. Mathar_, Mar 20 2018
%F Sum_{n>=0} (-1)^n/a(n) = sqrt(3)*Pi/27 - log(2)/9. - _Amiram Eldar_, Dec 12 2021
%t Range[6, 1000, 9] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t LinearRecurrence[{2,-1},{6,15},60] (* _Harvey P. Dale_, Feb 01 2014 *)
%o (Magma) [9*n+6: n in [0..60]]; // _Vincenzo Librandi_, Jul 24 2011
%o (PARI) a(n)=9*n+6 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A008591, A017209, A017221.
%K nonn,easy
%O 0,1
%A David J. Horn and Laura Krebs Gordon (lkg615(AT)verizon.net), 1985
|
