OFFSET
1,1
COMMENTS
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.
REFERENCES
A. K. Devaraj, "Euler's generalisation of Fermat's theorem - a further generalisation" - Hawaii International conference on Mathematics & Statistics (2004). [ISSN 15503747]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..300
Index entries for linear recurrences with constant coefficients, signature (1025,-1024).
FORMULA
G.f. -x*(-373+1024*x) / ( (1024*x-1)*(x-1) ). - R. J. Mathar, Oct 08 2011
MATHEMATICA
(4^(5*Range[15]+1)+7)/11 (* Paolo Xausa, Mar 20 2024 *)
PROG
(PARI) a(n)=(4^(5*n+1) + 7)/11 \\ Charles R Greathouse IV, Oct 05 2011
(Magma) [(4^(5*n+1) + 7)/11 : n in [1..15]]; // Vincenzo Librandi, Oct 06 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
A.K. Devaraj, Dec 05 2009
STATUS
approved