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

0,3

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

Table of n, a(n) for n=0..86.

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).

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

Mathematica

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

Prog

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

Crossrefs

Cf. A204671, A174824.

Sequence in context: A291379 A001138 A133587 * A204817 A199721 A349942

Adjacent sequences: A204690 A204691 A204692 * A204694 A204695 A204696

Keyword

nonn,easy

Author

José María Grau Ribas, Jan 18 2012

Status

approved