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A004770
Numbers of the form 8k+5; or, numbers whose binary expansion ends in 101.
30
5, 13, 21, 29, 37, 45, 53, 61, 69, 77, 85, 93, 101, 109, 117, 125, 133, 141, 149, 157, 165, 173, 181, 189, 197, 205, 213, 221, 229, 237, 245, 253, 261, 269, 277, 285, 293, 301, 309, 317, 325, 333, 341, 349, 357, 365, 373, 381, 389, 397, 405, 413, 421, 429
OFFSET
1,1
COMMENTS
Only numbers of the form 8k+5 may be written as a sum of 5 odd squares. Examples: 5 = 1+1+1+1+1, 13 = 9+1+1+1+1, 21 = 9+9+1+1+1, 29 = 25+1+1+1+1= 9+9+9+1+1, 37 = 9+9+9+9+1 = 25+9+1+1+1, 45 = 25+9+9+1+1=9+9+9+9+9, 53 = 49+1+1+1+1 = 25+25+1+1+1 = 25+9+9+9+1, ... - Philippe Deléham, Sep 03 2005
Positive solutions to the equation x == 5 (mod 8). - K.V.Iyer, Apr 27 2009
FORMULA
From R. J. Mathar, Mar 14 2011: (Start)
a(n) = 8*n - 3.
G.f.: x*(5+3*x)/(x-1)^2. (End)
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, May 28 2011
MATHEMATICA
Range[5, 1000, 8] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)
LinearRecurrence[{2, -1}, {5, 13}, 60] (* or *) NestList[#+8&, 5, 60] (* Harvey P. Dale, Jun 28 2021 *)
PROG
(Magma) [8*n-3: n in [1..60]]; // Vincenzo Librandi, May 28 2011
(Haskell)
a004770 = (subtract 3) . (* 8)
a004770_list = [5, 13 ..] -- Reinhard Zumkeller, Aug 17 2012
(PARI) a(n)=8*n-3 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Cf. A004776 (complement), A007521 (primes).
Sequence in context: A007675 A043441 A251537 * A191155 A107996 A107997
KEYWORD
nonn,easy
STATUS
approved