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

1,2

Comments

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

Links

Table of n, a(n) for n=1..61.

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A047527, A103192.

Sequence in context: A102582 A351296 A089168 * A103192 A097856 A071593

Adjacent sequences: A103124 A103125 A103126 * A103128 A103129 A103130

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 25 2005

Status

approved