A114753 a(n) = n if odd, else 2n-1.

1, 3, 3, 7, 5, 11, 7, 15, 9, 19, 11, 23, 13, 27, 15, 31, 17, 35, 19, 39, 21, 43, 23, 47, 25, 51, 27, 55, 29, 59, 31, 63, 33, 67, 35, 71, 37, 75, 39, 79, 41, 83, 43, 87, 45, 91, 47, 95, 49, 99, 51, 103, 53, 107, 55, 111, 57, 115, 59, 119, 61, 123, 63, 127, 65, 131, 67, 135, 69

Offset

1,2

Comments

Original name: First column of A114751.

First column of table A210530. - Boris Putievskiy, Jan 29 2013

Links

Table of n, a(n) for n=1..69.

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Formula

a(2n+1) = 2n+1, a(2n) = 4n-1.

a(n) = 2*a(n-2) - a(n-4). - Joerg Arndt, Apr 02 2011

Equals A133080 * [1,2,3,...]. - Gary W. Adamson, Sep 08 2007

A114752(n) + a(n) - 1 = 3*n-2. - Gary W. Adamson, Sep 16 2007

G.f. x*(1+3*x+x^2+x^3) / ( (x-1)^2*(1+x)^2 ). - R. J. Mathar, Apr 04 2012

a(n) = (3*n-1-(n-1)*(-1)^(n-1))/2. - Boris Putievskiy, Jan 29 2013

Mathematica

Table[If[OddQ[n], n, 2n-1], {n, 1, 120}] (* Vladimir Joseph Stephan Orlovsky, Apr 02 2011*)

Prog

(PARI) apply( {A114753(n)=if(n%2, n, 2*n-1)}, [1..77]) \\ M. F. Hasler, Jun 04 2026
(Python)
def A114753(n): return n if n&1 else (n<<1)-1 # Chai Wah Wu, Jun 04 2026

Crossrefs

Cf. A114751, A114752.

Cf. A133080, A210530.

Sequence in context: A318461 A085379 A070801 * A079316 A394513 A106481

Adjacent sequences: A114750 A114751 A114752 * A114754 A114755 A114756

Keyword

easy,nonn

Author

Amarnath Murthy, Nov 15 2005

Extensions

More terms from Joshua Zucker, May 05 2006

Explicit definition by M. F. Hasler, Jun 04 2026

Status

approved