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%I #48 Jan 28 2023 12:46:04
%S 13,29,45,61,77,93,109,125,141,157,173,189,205,221,237,253,269,285,
%T 301,317,333,349,365,381,397,413,429,445,461,477,493,509,525,541,557,
%U 573,589,605,621,637,653,669,685,701,717,733,749,765,781,797,813,829,845
%N a(n) = 16n + 13.
%C Solutions to (7^x + 11^x) mod 17 = 13.
%C a(n-2), n>=2, gives the second column in triangle A238476 related to the Collatz problem. - _Wolfdieter Lang_, Mar 12 2014
%H Vincenzo Librandi, <a href="/A082285/b082285.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 Leo Tavares, <a href="/A082285/a082285.jpg">Illustration: Bounded Star Crosses</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 16*n + 13.
%F a(n) = 32*n - a(n-1) + 10; a(0)=13. - _Vincenzo Librandi_, Oct 10 2011
%F From _Stefano Spezia_, Dec 27 2019: (Start)
%F O.g.f.: (13 + 3*x)/(1 - x)^2.
%F E.g.f.: exp(x)*(13 + 16*x).
%F (End)
%F a(n) = A008594(n+1) + A016813(n+1) - 4. - _Leo Tavares_, Sep 22 2022
%t Range[13, 1000, 16] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)
%t LinearRecurrence[{2,-1},{13,29},60] (* _Harvey P. Dale_, Jan 28 2023 *)
%o (PARI) \\ solutions to 7^x+11^x == 13 mod 17
%o anpbn(n) = { for(x=1,n, if((7^x+11^x-13)%17==0,print1(x" "))) }
%o (Magma) [[ n : n in [1..1000] | n mod 16 eq 13]]; // _Vincenzo Librandi_, Oct 10 2011
%Y Cf. A008598, A119413, A106839, A098502.
%Y Cf. A008594, A016813.
%K easy,nonn
%O 0,1
%A _Cino Hilliard_, May 10 2003
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