login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A017197 a(n) = 9*n + 3. 14
3, 12, 21, 30, 39, 48, 57, 66, 75, 84, 93, 102, 111, 120, 129, 138, 147, 156, 165, 174, 183, 192, 201, 210, 219, 228, 237, 246, 255, 264, 273, 282, 291, 300, 309, 318, 327, 336, 345, 354, 363, 372, 381, 390, 399, 408, 417, 426, 435, 444, 453, 462, 471, 480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Numbers whose digital root is 3. - Cino Hilliard, Dec 26 2006

a(n)^2 = A017198(n). - Reinhard Zumkeller, Jul 13 2010

For all n, a(n) is not a^2 + b^2. - Vincenzo Librandi, Nov 20 2010

LINKS

Table of n, a(n) for n=0..53.

Tanya Khovanova, Recursive Sequences

Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081, 2014

Index entries for linear recurrences with constant coefficients, signature (2,-1).

FORMULA

a(n) = 9 + a(n-1).

a(n) = 3*A016777(n).

a(n) = A092292(n) + A092293(n) + A092296(n).

Sum_{n>=0} (-1)^n / a(n) = (Pi / sqrt(3) + log(2))/9. G.f.: 3*(1+2*x) / (1-x)^2. - Philippe Deléham, Mar 10 2004

a(n) = 3*(6*n-1) - a(n-1) with a(0)=3. - Vincenzo Librandi, Nov 20 2010

MATHEMATICA

q=3; lst={}; Do[AppendTo[lst, (q*n+1)*q], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 16 2009 *)

PROG

(PARI) threesome(n) = { local(x, ln, j, f); for(x=1, n, f=0; ln=length(Str(x)); if(droot(x)==3, print1(x", ")); ) } droot(n) = \ the digital root of a number. { local(x); x= n%9; if(x>0, return(x), return(9)) } \\ Cino Hilliard, Dec 26 2006

(Sage) [i+3 for i in range(480) if gcd(i, 9) == 9] # Zerinvary Lajos, May 20 2009

(Haskell)

a017197 = (+ 3) . (* 9)

a017197_list = [3, 12 ..]  -- Reinhard Zumkeller, Jun 04 2015

CROSSREFS

Cf. A092292, A092293, A092296.

Cf. sequences with general form q*(q*n+1): A016825 (q=2), this sequence (q=3), A119413 (q=4), ... - Vladimir Joseph Stephan Orlovsky, Feb 16 2009

Cf. A016777.

Sequence in context: A074276 A055041 A061819 * A051369 A069538 A052217

Adjacent sequences:  A017194 A017195 A017196 * A017198 A017199 A017200

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Cino Hilliard, Dec 26 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 26 18:46 EDT 2017. Contains 284137 sequences.