%I #24 Mar 20 2024 07:53:22

%S 373,381301,390451573,399822410101,409418147942773,419244183493398901,

%T 429306043897240473973,439609388950774245347701,

%U 450160014285592827236045173,460963854628447055089710256501,472026987139529784411863302656373

%N a(n) = (4^(5*n+1) + 7)/11.

%C In A165806, A165808 & A165809 a congruence property of polynomial functions was demonstrated. In the present sequence a congruence property of exponential functions is demonstrated. Let the function be f(n) = 2^n + 7. Then f(n + k*phi(f(n))) is congruent to 0 mod(f(n)). This is a sequence of quotients generated by (f(n + k*phi f(n)))/f(n) when n = 2.

%D A. K. Devaraj, "Euler's generalisation of Fermat's theorem - a further generalisation" - Hawaii International conference on Mathematics & Statistics (2004). [ISSN 15503747]

%H Vincenzo Librandi, <a href="/A171216/b171216.txt">Table of n, a(n) for n = 1..300</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1025,-1024).

%F G.f. -x*(-373+1024*x) / ( (1024*x-1)*(x-1) ). - _R. J. Mathar_, Oct 08 2011

%t (4^(5*Range[15]+1)+7)/11 (* _Paolo Xausa_, Mar 20 2024 *)

%o (PARI) a(n)=(4^(5*n+1) + 7)/11 \\ _Charles R Greathouse IV_, Oct 05 2011

%o (Magma) [(4^(5*n+1) + 7)/11 : n in [1..15]]; // _Vincenzo Librandi_, Oct 06 2011

%K nonn,easy

%O 1,1

%A _A.K. Devaraj_, Dec 05 2009