A137708 - OEIS

A137708

Secondary Lower Wythoff Sequence.

1, 2, 5, 6, 7, 8, 11, 12, 15, 16, 17, 18, 21, 22, 23, 24, 27, 28, 31, 32, 33, 34, 37, 38, 41, 42, 43, 44, 47, 48, 49, 50, 53, 54, 57, 58, 59, 60, 63, 64, 65, 66, 69, 70, 73, 74, 75, 76, 79, 80, 83, 84, 85, 86, 89, 90, 91, 92, 95, 96, 99, 100, 101, 102, 105, 106, 109, 110, 111

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

This sequence is the ordered union of odd numbered columns of the Wythoff secondary array, A137707. See A137707 for complementary equations of which this sequence is a solution.

LINKS

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

FORMULA

a(2n)=2*A000201(n)=a(2n-1)+1; A000201 is the lower Wythoff sequence.

EXAMPLE

The lower Wythoff sequence begins with 1,3,4,6,8,9,...

Double these: 2,6,8,12,16,18...; subtract 1: 1,5,7,11,15,17;

Then merge: 1,2,5,6,7,8,11,12,15,16,17,18,...

PROG

(Python)

from math import isqrt

def A137708(n): return ((m:=n+1>>1)+isqrt(5*m**2)&-2)-(n&1) # Chai Wah Wu, Aug 11 2022