A022801 n-th Lucas number (A000204(n)) + n-th non-Lucas number (A090946(n+1)).

3, 8, 10, 15, 20, 28, 41, 60, 90, 138, 215, 339, 540, 863, 1385, 2229, 3594, 5802, 9374, 15153, 24503, 39631, 64109, 103713, 167793, 271476, 439238, 710682, 1149887, 1860535, 3010387, 4870886, 7881236, 12752084, 20633281, 33385325, 54018565

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Formula

a(n) = A000204(n) + A090946(n + 1). - Sean A. Irvine, May 21 2019

Maple

with(combinat): lucas:= n->fibonacci(n+1)+fibonacci(n-1): n:=1: for k from 1 to 7 do for nonlucas from lucas(k)+1 to lucas(k+1)-1 do printf("%d, ", nonlucas+lucas(n)) :n:=n+1 od od: # C. Ronaldo (aga_new_ac(AT)hotmail.com)

Mathematica

Module[{nn=40, luc, nluc}, luc=LucasL[Range[nn]]; nluc=Complement[Range[ Last[ luc]], luc]; Total/@Thread[{luc, Take[nluc, Length[luc]]}]] (* Harvey P. Dale, May 02 2019 *)

Prog

(Python)
from sympy import lucas
def A022801(n):
    def f(x):
        if x<=2: return n+1
        a, b, c = 1, 3, 0
        while b<=x:
            a, b = b, a+b
            c += 1
        return n+1+c
    m, k = n+1, f(n+1)
    while m != k: m, k = k, f(k)
    return m+lucas(n) # Chai Wah Wu, Sep 10 2024

Crossrefs

Sequence in context: A047356 A083246 A023492 * A128699 A104816 A181022

Adjacent sequences: A022798 A022799 A022800 * A022802 A022803 A022804

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

Thanks to Karima MOUSSAOUI (bouyao(AT)wanadoo.fr), who noticed that there were two versions of this sequence, differing at about the 22nd term, Feb 28 2004

More terms from Emeric Deutsch, Jan 14 2005

Status

approved