A075123 a(n) is the least positive integer > a(n-1) and a(n) is not 2*a(i)+a(j) for 1<=i

1, 2, 3, 6, 9, 14, 17, 22, 25, 30, 33, 38, 41, 46, 49, 54, 57, 62, 65, 70, 73, 78, 81, 86, 89, 94, 97, 102, 105, 110, 113, 118, 121, 126, 129, 134, 137, 142, 145, 150, 153, 158, 161, 166, 169, 174, 177, 182, 185, 190, 193, 198, 201, 206, 209, 214, 217, 222, 225, 230

Offset: 1

Author

Floor van Lamoen, Sep 02 2002

Keywords

• nonn
• easy

Comments

a(n) = A047452(n-2) for n > 3 because of first formula. - Georg Fischer, Oct 19 2018

Links

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

Crossrefs

Cf. A003278, A026471, A033627, A047452, A075122.

Programs

Mathematica

Join[{1,2,3},Table[4n-10-Mod[n,2],{n,4,60}]] (* or *)
LinearRecurrence[ {1,1,-1},{1,2,3,6,9,14},60] (* Harvey P. Dale, Oct 28 2012 *)

Python

def A075123(n): return (n-2<<2)-2-(n&1) if n>3 else n # Chai Wah Wu, Mar 30 2024

Formula

a(n) = 4n - 10 - (n mod 2), for n>3. - Ralf Stephan, Nov 16 2004

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3. - Harvey P. Dale, Oct 28 2012

G.f.: x*(1+x+2*x^3+2*x^4+2*x^5)/((1+x)*(1-x)^2). - Georg Fischer, May 15 2019