A004770 - OEIS

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

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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 *)