A103127 Numbers congruent to {-1, 1, 3, 5} mod 16.

1, 3, 5, 15, 17, 19, 21, 31, 33, 35, 37, 47, 49, 51, 53, 63, 65, 67, 69, 79, 81, 83, 85, 95, 97, 99, 101, 111, 113, 115, 117, 127, 129, 131, 133, 143, 145, 147, 149, 159, 161, 163, 165, 175, 177, 179, 181, 191, 193, 195, 197, 207, 209, 211, 213, 223, 225, 227, 229, 239, 241

Offset: 1

Author

N. J. A. Sloane, Mar 25 2005

Keywords

• nonn
• easy

Comments

Agrees with A103192 for the first 511 terms, but then diverges (see comment in A103192). - Bruno Berselli, Dec 01 2016

Links

• David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers, J. Integer Seq. 8 (2005), no. 3, Article 05.3.6, 15 pp [pdf, ps].
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
• Index entries for sequences which agree for a long time but are different

Crossrefs

Cf. A047527, A103192.

Programs

Haskell

a103127 n = a103127_list !! (n-1)
a103127_list = [x | x <- [1..], x `mod` 16 `elem` [1,3,5,15]]
-- Reinhard Zumkeller, Jul 21 2012

Mathematica

Select[Range[300],MemberQ[{1,3,5,15},Mod[#,16]]&] (* Harvey P. Dale, Aug 10 2019 *)

Formula

a(n) = 2*A047527(n) + 1.

From R. J. Mathar, Aug 30 2008: (Start)

O.g.f.: x*(1 + 2*x + 2*x^2 + 10*x^3 + x^4)/((1 - x)^2*(1 + x)*(1 + x^2)).

a(n) = a(n-4) + 16. (End)

a(n) = 2*A047476(n+1) - 1. - Philippe Deléham, Dec 01 2016