A054966 Numbers that are congruent to {0, 1, 8} mod 9.

0, 1, 8, 9, 10, 17, 18, 19, 26, 27, 28, 35, 36, 37, 44, 45, 46, 53, 54, 55, 62, 63, 64, 71, 72, 73, 80, 81, 82, 89, 90, 91, 98, 99, 100, 107, 108, 109, 116, 117, 118, 125, 126, 127, 134, 135, 136, 143, 144, 145, 152, 153, 154, 161, 162, 163, 170, 171, 172, 179, 180

Offset

1,3

Comments

n == n^3 mod 9, so the iterated sum of the decimal digits of n and n^3 are equal.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

H. I. Okagbue, M. O. Adamu, S. A. Bishop and A. A. Opanuga, Properties of Sequences Generated by Summing the Digits of Cubed Positive Integers, Indian Journal Of Natural Sciences, Vol. 6, Issue 32, October 2015.

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

Formula

G.f.: x^2*(1+7*x+x^2) / ((1+x+x^2)*(x-1)^2). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jun 14 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3).

a(3k) = 9k-1, a(3k-1) = 9k-8, a(3k-2) = 9k-9. (End)

A008591 UNION A056020. - R. J. Mathar, Jul 19 2024

a(n) -a(n-1) = A105395(n+1), n>1. - R. J. Mathar, Jul 19 2024

Maple

A054966:=n->3*n-3+2*cos(2*n*Pi/3)+2*sin(2*n*Pi/3)/sqrt(3): seq(A054966(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016

Mathematica

Select[Range[0, 200], MemberQ[{0, 1, 8}, Mod[#, 9]] &] (* Wesley Ivan Hurt, Jun 14 2016 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 1, 8, 9}, 100] (* Vincenzo Librandi, Jun 15 2016 *)

Prog

(Magma) [n : n in [0..200] | n mod 9 in [0, 1, 8]]; // Wesley Ivan Hurt, Jun 14 2016

Crossrefs

Cf. A047523. Complement of A275910. Distinct terms of A004164.

Sequence in context: A334728 A070480 A135043 * A130881 A235399 A283628

Adjacent sequences: A054963 A054964 A054965 * A054967 A054968 A054969

Keyword

nonn,easy

Author

Henry Bottomley, May 24 2000

Status

approved