A337211 Numbers k such that b(k) < b(j) for all j < k where b(k) = Min_{sqrt(n) - Sum_{i} sqrt(c_i) > 0 with c_i being unique integers}.

1, 2, 3, 4, 5, 6, 10, 12, 14, 15, 18, 21, 22, 24, 26, 29, 34, 35, 38, 40, 42, 46, 47, 79, 89, 184, 226, 264, 269, 299, 419, 426, 505, 545

Offset: 1

Author

Robert G. Wilson v, Aug 19 2020

Keywords

• nonn
• more

Comments

This sequence is the original definition of A045880.

Examples

			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.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..34
• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A045880, A333987, A337210.

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