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A137708 Secondary Lower Wythoff Sequence. 3
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
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
CROSSREFS
Sequence in context: A047269 A039027 A129816 * A122806 A122546 A258775
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 07 2008
EXTENSIONS
a(37)=59 corrected by Georg Fischer, Nov 24 2022
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)