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A054966 Numbers that are congruent to {0, 1, 8} mod 9. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

REFERENCES

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

LINKS

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

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)

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.

Sequence in context: A069237 A070480 A135043 * A130881 A235399 A283628

Adjacent sequences:  A054963 A054964 A054965 * A054967 A054968 A054969

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, May 24 2000

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.