A111952 a(n) = 3*n mod 7.

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

Offset

0,2

Comments

Period 7: repeat [0, 3, 6, 2, 5, 1, 4].

Draw a regular heptagon with vertices labeled 0..6 going clockwise. Choose any seven consecutive values of a(n) and connect the corresponding vertices in that order with straight lines. This results in a clockwise-inscribed seven-pointed star that remains unbroken during construction. - Wesley Ivan Hurt, Apr 10 2015

Links

Table of n, a(n) for n=0..89.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Formula

G.f.: (3*x+6*x^2+2*x^3+5*x^4+x^5+4*x^6)/(1-x^7).

a(n) = mod(n*(7*n-1)/2, 7) = mod(A022264(n), 7).

Recurrence: a(n) = a(n-7) for n > 6. - Wesley Ivan Hurt, Apr 10 2015

a(n) = (21 + 4*(n mod 7) - 3*((n+1) mod 7) + 4*((n+2) mod 7) - 3*((n+3) mod 7) + 4*((n+4) mod 7) - 3*((n+5) mod 7) - 3*((n+6) mod 7))/7. - Wesley Ivan Hurt, Dec 23 2016

a(n) = A010876(3*n). - R. J. Mathar, Jan 15 2021

Maple

A111952:=n->3*n mod 7: seq(A111952(n), n=0..100); # Wesley Ivan Hurt, Apr 10 2015

Mathematica

Mod[3 Range[0, 100], 7] (* Wesley Ivan Hurt, Apr 10 2015 *)

Prog

(PARI) a(n)=3*n%7 \\ Charles R Greathouse IV, Jul 23, 2011
(Magma) [3*n mod 7 : n in [0..100]]; // Wesley Ivan Hurt, Apr 10 2015

Crossrefs

Cf. A022264.

Sequence in context: A333010 A319513 A160590 * A068466 A194076 A194040

Adjacent sequences: A111949 A111950 A111951 * A111953 A111954 A111955

Keyword

easy,nonn

Author

Paul Barry, Aug 22 2005

Status

approved