A144396 The odd numbers greater than 1.

3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131, 133

Offset

1,1

Comments

Last number of the n-th row of the triangle described in A142717.

If negated, these are also the values at local minima of the sequence A141620.

a(n) is the shortest leg of the n-th Pythagorean triple with consecutive longer leg and hypotenuse. The n-th such triple is given by (2n+1,2n^2+2n, 2n^2+2n+1), so that the longer legs are A046092(n) and the hypotenuses are A099776(n). - Ant King, Feb 10 2011

Numbers k such that the symmetric representation of sigma(k) has a pair of bars as its ends (cf. A237593). - Omar E. Pol, Sep 28 2018

Numbers k such that there is a prime knot with k crossings and braid index 2. (IS this true with "prime" removed?) - Charles R Greathouse IV, Feb 14 2023

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = A005408(n+1) = A000290(n+1) - A000290(n).

G.f.: x*(3-x)/(1-x)^2. - Jaume Oliver Lafont, Aug 30 2009

a(n) = A254858(n-1,2). - Reinhard Zumkeller, Feb 09 2015

Maple

seq(n, n=3..200, 2); # Muniru A Asiru, Sep 28 2018

Mathematica

Range[3, 200, 2] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2012 *)

Prog

(Haskell)
a144396 = (+ 1) . (* 2)
a144396_list = [3, 5 ..] -- Reinhard Zumkeller, Feb 09 2015
(GAP) List([3, 5..200], n->n); # Muniru A Asiru, Sep 28 2018
(PARI) a(n)=2*n+1 \\ Charles R Greathouse IV, Feb 14 2023

Crossrefs

Complement of A004275 and of A004277.

Cf. A000217, A002378, A005408, A007395, A046092, A099776, A237593, A254858.

Essentially the same as A140139, A130773, A062545, A020735, A005818.

Sequence in context: A004273 A005408 A176271 * A060747 A089684 A283002

Adjacent sequences: A144393 A144394 A144395 * A144397 A144398 A144399

Keyword

nonn,easy,less

Author

Paul Curtz, Oct 03 2008

Extensions

Edited by R. J. Mathar, May 21 2009

Status

approved