OFFSET
1,2
COMMENTS
This sequence is the original definition of A045880.
LINKS
Sean A. Irvine, Table of n, a(n) for n = 1..34
Sean A. Irvine, Java program (github)
EXAMPLE
a(1) is 1 since sqrt(1) - sqrt(0) = 1.00000 ... ;
a(2) is 2 since sqrt(2) - sqrt(1) = 0.41421 ... which is an improvement over a(0);
a(3) is 3 since sqrt(3) - sqrt(2) = 0.31783 ... ;
a(4) is 4 since sqrt(4) - sqrt(3) = 0.26794 ... ;
a(5) is 5 since sqrt(5) - sqrt(4) = 0.23606 ... ;
a(6) is 6 since sqrt(6) - (sqrt(1) + sqrt(2)) = 0.03527 ... ;
7 is not in the sequence since sqrt(7) - sqrt(6) = 0.19626 ... which is not an improvement of a(5);
8 is not in the sequence since sqrt(8) - (sqrt(1) + sqrt(3)) = 0.09637 ... which again is not an improvement over a(5);
9 is not in the sequence since sqrt(9) - sqrt(8) = 0.17157 ... which is not an improvement of a(5);
a(7) is 10 because sqrt(10) - (sqrt(2) + sqrt(3)) = 0.01601 ... ;
a(8) is 12 because sqrt(12) - (sqrt(1) + sqrt(6)) = 0.01461 ... ; etc.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Robert G. Wilson v, Aug 19 2020
EXTENSIONS
a(24) corrected by Jinyuan Wang, Aug 23 2020
Title improved, a(26) corrected and a(31)-a(34) from Sean A. Irvine, Mar 23 2021
STATUS
approved