|
Search: id:A056020
|
|
|
| A056020 |
|
Numbers n that are congruent to +-1 mod 9. |
|
+0
10
|
|
| 1, 8, 10, 17, 19, 26, 28, 35, 37, 44, 46, 53, 55, 62, 64, 71, 73, 80, 82, 89, 91, 98, 100, 107, 109, 116, 118, 125, 127, 134, 136, 143, 145, 152, 154, 161, 163, 170, 172, 179, 181, 188, 190, 197, 199, 206, 208, 215, 217, 224, 226, 233, 235, 242, 244, 251, 253
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Or, numbers n such that n^2 == 1 (mod 9).
Or, numbers n such that the iterative cycle k -> sum of digits of k^2 when started at n contains a 1. E.g. 8 -> 6+4 = 10 -> 1+0+0 = 1 and 17 -> 2+8+9 = 19 -> 3+6+1 = 10 -> 1+0+0 = 1. - Asher Auel (asher.auel(AT)reed.edu), May 17 2001
Except for the first term of [A132355] (0,7,11,32,40,...) and [A056020] (1,8,10,17,19,...,], if X=[A056020], Y=[A010701] (3,3,3,3,.) and A=[A132355], we have for all other terms, Pell's equation X^2-A*Y^2=1. Example: 8^2-7*3^2=1; 10^2-11*3^2=1; 17^2-32*3^2=1; 19^2-40*3^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
|
|
LINKS
|
Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
|
|
FORMULA
|
a(1) = 1; a(n) = 9(n-1) - a(n-1) - Rolf Pleisch (r_pleisch(AT)gmx.ch), Jan 31 2008 [Offset corrected by Jon Schoenfield, Dec 22 2008]
O.g.f.: 1+5/[4(x+1)]+27/[4(-1+x)]+9/[2(-1+x)^2] . a(n+1)-a(n) = A010697(n). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 10 2008
|
|
MATHEMATICA
|
Select[ Range[ 300 ], PowerMod[ #, 2, 3^2 ]==1& ]
|
|
CROSSREFS
|
Cf. A007953, A004159, A061903 - A061910.
Cf. A010701, A132355 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A165143 A038209 A061908 this_sequence A049510 A121846 A059094
Adjacent sequences: A056017 A056018 A056019 this_sequence A056021 A056022 A056023
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 08 2000
|
|
|
Search completed in 0.002 seconds
|
