A004770 Numbers of the form 8k+5; or, numbers whose binary expansion ends in 101.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Tanya Khovanova, Recursive Sequences.

Index entries for linear recurrences with constant coefficients, signature (2,-1)

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. A110534, A017101, A017113.

Cf. A004776 (complement), A007521 (primes).

Sequence in context: A007675 A043441 A251537 * A191155 A107996 A107997

Adjacent sequences: A004767 A004768 A004769 * A004771 A004772 A004773

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved