%I #71 Oct 05 2024 14:05:17
%S 5,14,23,32,41,50,59,68,77,86,95,104,113,122,131,140,149,158,167,176,
%T 185,194,203,212,221,230,239,248,257,266,275,284,293,302,311,320,329,
%U 338,347,356,365,374,383,392,401,410,419,428,437,446,455,464,473,482
%N a(n) = 9*n + 5.
%C Numbers whose digital root is 5. - _Halfdan Skjerning_, Mar 15 2018
%D R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section D5.
%H Vincenzo Librandi, <a href="/A017221/b017221.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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F G.f.: (5+4*x)/(1-x)^2. - _R. J. Mathar_, Mar 20 2018
%F From _G. C. Greubel_, Jan 06 2023: (Start)
%F a(n) = a(n-1) + 9, with a(0) = 5.
%F E.g.f.: (5 + 9*x)*exp(x). (End)
%p seq(9*w+5, w=0..100); # _Matt C. Anderson_, May 18 2017
%t Range[5, 1000, 9] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)
%t 9*Range[0,60]+5 (* or *) LinearRecurrence[{2,-1},{5,14},60] (* _Harvey P. Dale_, Jul 05 2021 *)
%o (PARI) forstep(n=5,500,9,print1(n", ")) \\ _Charles R Greathouse IV_, May 28 2011
%o (Magma) [9*n+5: n in [0..60]]; // _Vincenzo Librandi_, Jul 24 2011
%o (SageMath) [9*n+5 for n in range(51)] # _G. C. Greubel_, Jan 06 2023
%Y Sequences of the form (9*n+5)^k: this sequence (k=1), A017222 (k=2), A017223 (k=3), A017224 (k=4), A017225 (k=5), A017226 (k=6), A017227 (k=7), A017228 (k=8), A017229 (k=9), A017230 (k=10), A017231 (k=11).
%Y Cf. A008591, A017209.
%Y Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_