

A017233


a(n) = 9*n + 6.


12



6, 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402, 411, 420, 429, 438, 447, 456, 465, 474, 483
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OFFSET

0,1


COMMENTS

General form: (q*n1)*q, cf. A017233 (q=3), A098502 (q=4).  Vladimir Joseph Stephan Orlovsky, Feb 16 2009
Numbers whose digital root is 6; that is, A010888(a(n)) = 6. (Ball essentially says that Iamblichus (circa 350) announced that a number equal to the sum of three integers 3n, 3n  1, and 3n  2 has 6 as what is now called the number's digital root.)  Rick L. Shepherd, Apr 01 2014


REFERENCES

W. W. R. Ball, A Short Account of the History of Mathematics, Sterling Publishing Company, Inc., 2001 (Facsimile Edition) [orig. pub. 1912], pages 110111.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences
Luis Manuel Rivera, Integer sequences and kcommuting permutations, arXiv preprint arXiv:1406.3081, 2014
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

G.f.: 3*(2+x)/(x1)^2 .  R. J. Mathar, Mar 20 2018


MATHEMATICA

Range[6, 1000, 9] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2, 1}, {6, 15}, 60] (* Harvey P. Dale, Feb 01 2014 *)


PROG

(MAGMA) [9*n+6: n in [0..60]]; // Vincenzo Librandi, Jul 24 2011
(PARI) a(n)=9*n+6 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

Cf. A008591, A017209, A017221.
Sequence in context: A274319 A043477 A055040 * A122709 A052220 A217747
Adjacent sequences: A017230 A017231 A017232 * A017234 A017235 A017236


KEYWORD

nonn,easy


AUTHOR

David J. Horn and Laura Krebs Gordon (lkg615(AT)verizon.net), 1985


STATUS

approved



