A047523 -id:A047523 - cp's OEIS frontend

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

Henry Bottomley, May 24 2000

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

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A047523. Complement of A275910.

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

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

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 *)

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

A054967 Numbers that are congruent to {0, 1, 9} mod 10.

Original entry on oeis.org

0, 1, 9, 10, 11, 19, 20, 21, 29, 30, 31, 39, 40, 41, 49, 50, 51, 59, 60, 61, 69, 70, 71, 79, 80, 81, 89, 90, 91, 99, 100, 101, 109, 110, 111, 119, 120, 121, 129, 130, 131, 139, 140, 141, 149, 150, 151, 159, 160, 161, 169, 170, 171, 179, 180, 181, 189, 190, 191, 199

Offset: 1

Henry Bottomley, May 24 2000

Numbers with last digit 0, 1, or 9. - Wesley Ivan Hurt, Jun 14 2016

Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A047523.

[n: n in [0..200] | n mod 10 in [0,1,9]]; // Vincenzo Librandi, Feb 24 2016

seq(seq(10*i+j, j=[0,1,9]), i=0..30); # Robert Israel, Feb 23 2016

Select[Range[0, 200], MemberQ[{0, 1, 9}, Mod[#, 10]] &] (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 1, 9, 10}, 60] (* Vincenzo Librandi, Feb 24 2016 *)

G.f.: x^2*(x^2+8*x+1)/((x-1)^2*(x^2+x+1)). - Robert Israel, Feb 23 2016
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, Feb 24 2016
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = (30*n-30+21*cos(2*n*Pi/3)+7*sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 10k-1, a(3k-1) = 10k-9, a(3k-2) = 10k-10. (End)

cp's OEIS Frontend

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

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