A204693 - OEIS

%I #24 Aug 31 2019 15:45:48

%S 1,1,4,6,4,3,1,0,1,1,4,2,1,6,0,1,2,5,1,5,1,0,1,4,1,4,4,6,0,1,1,3,2,6,

%T 1,0,1,2,2,1,2,6,0,1,4,6,4,3,1,0,1,1,4,2,1,6,0,1,2,5,1,5,1,0,1,4,1,4,

%U 4,6,0,1,1,3,2,6,1,0,1,2,2,1,2,6,0,1,4

%N a(n) = n^n (mod 7).

%C For n>0, periodic with period 42 = A174824(7): repeat[1, 4, 6, 4, 3, 1, 0, 1, 1, 4, 2, 1, 6, 0, 1, 2, 5, 1, 5, 1, 0, 1, 4, 1, 4, 4, 6, 0, 1, 1, 3, 2, 6, 1, 0, 1, 2, 2, 1, 2, 6, 0].

%H <a href="/index/Rec#order_42">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F a(n) = a(n-42), n>42. - _R. J. Mathar_, Sep 25 2014

%F G.f.: ( -1 -4*x -2*x^37 -6*x^2 -4*x^22 -4*x^24 -4*x^25 -6*x^26 -x^28 -x^29 -3*x^30 -6*x^40 -2*x^31 -6*x^32 -x^33 -x^35 -x^17 -5*x^18 -x^19 -x^21 -x^23-x^38 -2*x^39 -2*x^36 -4*x^3 -3*x^4 -x^5 -x^7 -x^8 -4*x^9 -2*x^10 -x^11 -6*x^12 -x^14 -2*x^15 -5*x^16 ) / ( (x-1) *(1+x^6+x^5+x^4+x^3+x^2+x) *(1+x+x^2) *(1-x+x^3-x^4+x^6-x^8+x^9-x^11+x^12) *(1+x) *(1-x+x^2-x^3+x^4-x^5+x^6) *(1-x+x^2)*(1+x-x^3-x^4+x^6-x^8-x^9+x^11+x^12) ). - _R. J. Mathar_, Sep 25 2014

%t Table[PowerMod[n,n,7], {n,0,100}]

%o (PARI) a(n)=lift(Mod(n,7)^n) \\ _Charles R Greathouse IV_, Jan 23 2012

%Y Cf. A204671, A174824.

%K nonn,easy

%O 0,3

%A _José María Grau Ribas_, Jan 18 2012