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A090771 Numbers that are congruent to {1, 9} mod 10. 18
1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69, 71, 79, 81, 89, 91, 99, 101, 109, 111, 119, 121, 129, 131, 139, 141, 149, 151, 159, 161, 169, 171, 179, 181, 189, 191, 199, 201, 209, 211, 219, 221, 229, 231, 239, 241, 249, 251, 259, 261, 269, 271, 279, 281 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Cf. property described by Gary Detlefs in A113801: more generally, these numbers are of the form (2*h*n+(h-4)*(-1)^n-h)/4 (h,n natural numbers), therefore ((2*h*n+(h-4)*(-1)^n-h)/4)^2-1==0 (mod h); in this case, a(n)^2-1==0 (mod 10). - Bruno Berselli, Nov 17 2010

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = (40* A057569(n) +1)^(1/2). - Gary Detlefs, Feb 22 2010

Contribution from Bruno Berselli, Sep 16 2010 - Nov 17 2010: (Start)

  G.f.: x*(1+8*x+x^2)/((1+x)*(1-x)^2).

  a(n) = (10*n+3*(-1)^n-5)/2.

  a(n) = -a(-n+1) = a(n-1)+a(n-2)-a(n-3) = a(n-2)+10.

  a(n) = 10*A000217(n-1)+1 - 2*sum(a(i), i=1..n-1) for n>1. (End)

a(n)=10*n-a(n-1)-10 (with a(1)=1). - Vincenzo Librandi, Nov 16 2010

a(n) = sqrt(10*A132356(n-1)+1). - Ivan N. Ianakiev, Nov 09 2012

PROG

(Haskell)

a090771 n = a090771_list !! (n-1)

a090771_list = 1 : 9 : map (+ 10) a090771_list

-- Reinhard Zumkeller, Jan 07 2012

CROSSREFS

Cf. A090298.

Cf. A056020 (n=1 or 8 mod 9), A175885 (n=1 or 10 mod 11).

Cf. A045468 (primes), A195142 (partial sums).

Cf. A005408, A047209, A007310, A047336, A047522, A091998, A175886, A175887.

Sequence in context: A077788 A137018 A182391 * A195572 A046259 A074345

Adjacent sequences:  A090768 A090769 A090770 * A090772 A090773 A090774

KEYWORD

nonn,easy

AUTHOR

Giovanni Teofilatto, Feb 07 2004

EXTENSIONS

Edited and extended by Ray Chandler, Feb 10 2004

STATUS

approved

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Last modified April 18 04:10 EDT 2014. Contains 240688 sequences.