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

Author

Paul Curtz, Oct 03 2008

Keywords

• nonn
• easy
• less

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)

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.

Programs

GAP

List([3,5..200],n->n); # Muniru A Asiru, Sep 28 2018

Haskell

a144396 = (+ 1) . (* 2)
a144396_list = [3, 5 ..] -- 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 *)

PARI

a(n)=2*n+1 \\ Charles R Greathouse IV, Feb 14 2023

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

Extensions

Edited by R. J. Mathar, May 21 2009