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A082285 a(n) = 16*n + 13.

%I A082285 #55 Apr 13 2025 08:19:43
%S A082285 13,29,45,61,77,93,109,125,141,157,173,189,205,221,237,253,269,285,
%T A082285 301,317,333,349,365,381,397,413,429,445,461,477,493,509,525,541,557,
%U A082285 573,589,605,621,637,653,669,685,701,717,733,749,765,781,797,813,829,845
%N A082285 a(n) = 16*n + 13.
%C A082285 Solutions to (7^x + 11^x) mod 17 = 13.
%C A082285 a(n-2), n>=2, gives the second column in triangle A238476 related to the Collatz problem. - _Wolfdieter Lang_, Mar 12 2014
%H A082285 Vincenzo Librandi, <a href="/A082285/b082285.txt">Table of n, a(n) for n = 0..10000</a>
%H A082285 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A082285 Leo Tavares, <a href="/A082285/a082285.jpg">Illustration: Bounded Star Crosses</a>.
%H A082285 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A082285 a(n) = 16*n + 13.
%F A082285 a(n) = 32*n - a(n-1) + 10; a(0)=13. - _Vincenzo Librandi_, Oct 10 2011
%F A082285 From _Stefano Spezia_, Dec 27 2019: (Start)
%F A082285 O.g.f.: (13 + 3*x)/(1 - x)^2.
%F A082285 E.g.f.: exp(x)*(13 + 16*x). (End)
%F A082285 a(n) = A008594(n+1) + A016813(n+1) - 4. - _Leo Tavares_, Sep 22 2022
%F A082285 From _Elmo R. Oliveira_, Apr 12 2025: (Start)
%F A082285 a(n) = 2*a(n-1) - a(n-2).
%F A082285 a(n) = A004770(2*n+2). (End)
%t A082285 Range[13, 1000, 16] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)
%t A082285 LinearRecurrence[{2,-1},{13,29},60] (* _Harvey P. Dale_, Jan 28 2023 *)
%o A082285 (PARI) \\ solutions to 7^x+11^x == 13 mod 17
%o A082285 anpbn(n) = { for(x=1,n, if((7^x+11^x-13)%17==0,print1(x" "))) }
%o A082285 (Magma) [[ n : n in [1..1000] | n mod 16 eq 13]]; // _Vincenzo Librandi_, Oct 10 2011
%Y A082285 Cf. A004770, A008594, A008598, A016813, A098502, A106839, A119413.
%K A082285 easy,nonn
%O A082285 0,1
%A A082285 _Cino Hilliard_, May 10 2003