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a(n) = 9*n + 5.
23

%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_