A141620 -id:A141620 - cp's OEIS frontend

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

Paul Curtz, Oct 03 2008

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

Muniru A Asiru, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1)

Complement of A004275 and of A004277.
Cf. A000217, A002378, A005408, A007395, A046092, A099776, A237593, A254858.
Essentially the same as A140139, A130773, A062545, A020735, A005818.

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

a144396 = (+ 1) . (* 2)
a144396_list = [3, 5 ..] -- Reinhard Zumkeller, Feb 09 2015

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

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

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

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

Edited by R. J. Mathar, May 21 2009

A133128 Triangle of first differences of A120070 with a leftmost column of A002522.

Original entry on oeis.org

2, 5, -3, 10, -3, -5, 17, -3, -5, -7, 26, -3, -5, -7, -9, 37, -3, -5, -7, -9, -11, 50, -3, -5, -7, -9, -11, -13, 65, -3, -5, -7, -9, -11, -13, -15, 82, -3, -5, -7, -9, -11, -13, -15, -17, 101, -3, -5, -7, -9, -11, -13, -15, -17, -19, 122, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, 145, -3, -5, -7, -9, -11, -13, -15, -17, -19, -21, -23, 170, -3, -5, -7, -9, -11, -13

Offset: 0

Paul Curtz, Aug 27 2008

The flattened triangle is essentially the same as A141620.

			The triangle starts
2;
5, -3;
10,-3,-5;
17,-3,-5,-7;
26,-3,-5,-7,-9;

A133128 := proc(n,m) if m>= 1 then -2*m-1 ; else (n+1)^2+1 ; fi; end: seq(seq(A133128(n,m),m=0..n),n=0..15) ; # R. J. Mathar, Nov 22 2009

T(n,0) = A002522(n+1).
T(n,m) = -2m-1, m>0 .
sum_{m=0..n} T(n,m) = 2 (row sums).
T(n,n) = -A005408(n), n>0.

Edited and extended by R. J. Mathar, Nov 22 2009

A158894 Sawtooth pattern of one, then two, then three, then four etc. consecutive odd numbers, starting each time at 3.

Original entry on oeis.org

3, 3, 5, 3, 5, 7, 3, 5, 7, 9, 3, 5, 7, 9, 11, 3, 5, 7, 9, 11, 13, 3, 5, 7, 9, 11, 13, 15, 3, 5, 7, 9, 11, 13, 15, 17, 3, 5, 7, 9, 11, 13, 15, 17, 19, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 3, 5, 7, 9, 11, 13, 15, 17, 19

Offset: 1

Paul Curtz, Mar 29 2009

Obtained from A158405 by deleting the 1's, or from A141620 by deleting the positive numbers and flipping all signs.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A158405, A141620, A000124.

sp[n_]:=Module[{cl=Range[3,51,2],l={}},Table[l=Join[l,Take[cl,i]], {i,n}];l ]; sp[15] (* Harvey P. Dale, Oct 30 2011 *)
Table[Range[3,2n+1,2],{n,15}]//Flatten (* Harvey P. Dale, Jun 27 2025 *)

forstep(m=3,9,2,forstep(n=3,m,2,print1(n", "))) \\ Charles R Greathouse IV, Oct 30 2011

a(A000124(i))=3, i>=0. - R. J. Mathar, Apr 04 2009

Edited by R. J. Mathar, Apr 04 2009

Corrected by Harvey P. Dale, Oct 30 2011

A158897 The elements of A059100 at indices of triangular numbers, padded with zeros.

Original entry on oeis.org

6, 0, 11, 0, 0, 18, 0, 0, 0, 27, 0, 0, 0, 0, 38, 0, 0, 0, 0, 0, 51, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 0, 0, 123, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 146, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 171, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 198, 0, 0, 0, 0, 0, 0

Offset: 1

Paul Curtz, Mar 29 2009

nonn

Cf. A144396.

a(t)=A059100(i+1) if t=A000217(i), else a(t)=0.

a(n)=A141620(n-1)+A158405(n+1).

Edited and extended by R. J. Mathar, Apr 04 2009

cp's OEIS Frontend

A144396 The odd numbers greater than 1.

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A133128 Triangle of first differences of A120070 with a leftmost column of A002522.

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Maple

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A158894 Sawtooth pattern of one, then two, then three, then four etc. consecutive odd numbers, starting each time at 3.

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Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A158897 The elements of A059100 at indices of triangular numbers, padded with zeros.

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