A017221 - OEIS

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

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OFFSET

0,1

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).

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)

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 *)

PROG

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

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

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

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, A017209.

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

Sequence in context: A085950 A350996 A043473 * A052219 A044057 A147825

Adjacent sequences: A017218 A017219 A017220 * A017222 A017223 A017224

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved