A017221 a(n) = 9*n + 5.

5, 14, 23, 32, 41, 50, 59, 68, 77, 86, 95, 104, 113, 122, 131, 140, 149, 158, 167, 176, 185, 194, 203, 212, 221, 230, 239, 248, 257, 266, 275, 284, 293, 302, 311, 320, 329, 338, 347, 356, 365, 374, 383, 392, 401, 410, 419, 428, 437, 446, 455, 464, 473, 482

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers whose digital root is 5. - Halfdan Skjerning, Mar 15 2018

References

• R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section D5.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Sequences of the form (9*n+5)^k: this sequence (k=1), A017222 (k=2), A017223 (k=3), A017224 (k=4), A017225 (k=5), A017226 (k=6), A017227 (k=7), A017228 (k=8), A017229 (k=9), A017230 (k=10), A017231 (k=11).

Cf. A008591, A016789, A017209.

Cf. similar sequences with closed form (2*k-1)*n+k listed in A269044.

Programs

Magma

[9*n+5: n in [0..60]]; // Vincenzo Librandi, Jul 24 2011

Maple

seq(9*w+5, w=0..100); # Matt C. Anderson, May 18 2017

Mathematica

Range[5, 1000, 9] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
9*Range[0,60]+5 (* or *) LinearRecurrence[{2,-1},{5,14},60] (* Harvey P. Dale, Jul 05 2021 *)

PARI

forstep(n=5,500,9,print1(n", ")) \\ Charles R Greathouse IV, May 28 2011

SageMath

[9*n+5 for n in range(51)] # G. C. Greubel, Jan 06 2023

Formula

G.f.: (5+4*x)/(1-x)^2. - R. J. Mathar, Mar 20 2018

From G. C. Greubel, Jan 06 2023: (Start)

a(n) = a(n-1) + 9, with a(0) = 5.

E.g.f.: (5 + 9*x)*exp(x). (End)

From Elmo R. Oliveira, Apr 10 2025: (Start)

a(n) = 2*a(n-1) - a(n-2).

a(n) = A016789(3*n+1). (End)