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%I #54 Dec 03 2022 12:48:57
%S 10,21,32,43,54,65,76,87,98,109,120,131,142,153,164,175,186,197,208,
%T 219,230,241,252,263,274,285,296,307,318,329,340,351,362,373,384,395,
%U 406,417,428,439,450,461,472,483,494,505,516,527,538,549,560,571,582
%N a(n) = 11*n + 10.
%C If k is any member of A045572, the sequence lists the numbers n such that (n^k+1)/11 is a nonnegative integer. See also A267541. - _Bruno Berselli_, Jan 16 2016
%H Vincenzo Librandi, <a href="/A017509/b017509.txt">Table of n, a(n) for n = 0..10000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=989">Encyclopedia of Combinatorial Structures 989</a>
%H Leo Tavares, <a href="/A017509/a017509.jpg">Illustration: Triangular Lines</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F From _G. C. Greubel_, Oct 29 2019: (Start)
%F G.f.: (10 + x)/(1-x)^2.
%F E.g.f.: (10 + 11*x)*exp(x).
%F a(n) = 2*a(n-1) - a(n-2). (End)
%F a(n) = A008591(n+1) + A005408(n). - _Leo Tavares_, Oct 25 2022
%p seq((11*n+10), n=0..60); # _G. C. Greubel_, Oct 29 2019
%t Range[10, 1000, 11] (* _Vladimir Joseph Stephan Orlovsky_, May 29 2011 *)
%t (11*Range[60] -1) (* _G. C. Greubel_, Oct 29 2019 *)
%o (Magma) [11*n+10: n in [0..60]]; // _Vincenzo Librandi_, Sep 18 2011
%o (PARI) a(n)=11*n+10 \\ _Charles R Greathouse IV_, Jul 10 2016
%o (Sage) [(11*n+10) for n in (0..60)] # _G. C. Greubel_, Oct 29 2019
%o (GAP) List([0..60], n-> (11*n+10)); # _G. C. Greubel_, Oct 29 2019
%o (Python)
%o def a(n): return 11*n + 10
%o print([a(n) for n in range(53)]) # _Michael S. Branicky_, Oct 21 2021
%Y Cf. A008593, A017401, A017413, A045572, A267541.
%Y Cf. A211013 (partial sums), A254322 (partial products).
%Y Powers of the form (11*n+10)^m: this sequence (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), A017514 (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).
%Y Cf. A008591, A005408.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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