A204693 a(n) = n^n (mod 7).

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, 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, 4, 6, 0, 1, 1, 3, 2, 6, 1, 0, 1, 2, 2, 1, 2, 6, 0, 1, 4

Offset: 0

Author

José María Grau Ribas, Jan 18 2012

Keywords

• nonn
• easy

Comments

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].

Links

• Index entries for linear recurrences with constant coefficients, 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).

Crossrefs

Cf. A204671, A174824.

Programs

Mathematica

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

PARI

a(n)=lift(Mod(n,7)^n) \\ Charles R Greathouse IV, Jan 23 2012

Formula

a(n) = a(n-42), n>42. - R. J. Mathar, Sep 25 2014

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