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A056020 Numbers that are congruent to +-1 mod 9. 27
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; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Or, numbers k such that k^2 == 1 (mod 9).
Or, numbers k such that the iterative cycle j -> sum of digits of j^2 when started at k 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, May 17 2001
LINKS
FORMULA
a(1) = 1; a(n) = 9(n-1) - a(n-1). - Rolf Pleisch, Jan 31 2008 [Offset corrected by Jon E. Schoenfield, Dec 22 2008]
From R. J. Mathar, Feb 10 2008: (Start)
O.g.f.: 1 + 5/(4(x+1)) + 27/(4(-1+x)) + 9/(2(-1+x)^2).
a(n+1) - a(n) = A010697(n). (End)
a(n) = (9*A132355(n) + 1)^(1/2). - Gary Detlefs, Feb 22 2010
From Bruno Berselli, Nov 17 2010: (Start)
a(n) = a(n-2) + 9, for n > 2.
a(n) = 9*A000217(n-1) + 1 - 2*Sum_{i=1..n-1} a(i), n > 1. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi/9)*cot(Pi/9) = A019676 * A019968. - Amiram Eldar, Dec 04 2021
E.g.f.: 1 + ((18*x - 9)*exp(x) + 5*exp(-x))/4. - David Lovler, Sep 04 2022
MATHEMATICA
Select[ Range[ 300 ], PowerMod[ #, 2, 3^2 ]==1& ]
PROG
(PARI) a(n)=9*(n>>1)+if(n%2, 1, -1) \\ Charles R Greathouse IV, Jun 29 2011
(PARI) for(n=1, 40, print1(9*n-8, ", ", 9*n-1, ", ")) \\ Charles R Greathouse IV, Jun 29 2011
(Haskell)
a056020 n = a056020_list !! (n-1)
a05602_list = 1 : 8 : map (+ 9) a056020_list
-- Reinhard Zumkeller, Jan 07 2012
CROSSREFS
Cf. A007953, A047522 (n=1 or 7 mod 8), A090771 (n=1 or 9 mod 10).
Cf. A129805 (primes), A195042 (partial sums).
Sequence in context: A038209 A319293 A061908 * A049510 A121846 A059094
KEYWORD
nonn,easy,changed
AUTHOR
Robert G. Wilson v, Jun 08 2000
STATUS
approved

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Last modified February 27 12:56 EST 2024. Contains 370375 sequences. (Running on oeis4.)