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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}.
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%I #24 Mar 23 2021 21:33:37

%S 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,

%T 184,226,264,269,299,419,426,505,545

%N 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}.

%C This sequence is the original definition of A045880.

%H Sean A. Irvine, <a href="/A337211/b337211.txt">Table of n, a(n) for n = 1..34</a>

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a337/A337211.java">Java program</a> (github)

%e a(1) is 1 since sqrt(1) - sqrt(0) = 1.00000 ... ;

%e a(2) is 2 since sqrt(2) - sqrt(1) = 0.41421 ... which is an improvement over a(0);

%e a(3) is 3 since sqrt(3) - sqrt(2) = 0.31783 ... ;

%e a(4) is 4 since sqrt(4) - sqrt(3) = 0.26794 ... ;

%e a(5) is 5 since sqrt(5) - sqrt(4) = 0.23606 ... ;

%e a(6) is 6 since sqrt(6) - (sqrt(1) + sqrt(2)) = 0.03527 ... ;

%e 7 is not in the sequence since sqrt(7) - sqrt(6) = 0.19626 ... which is not an improvement of a(5);

%e 8 is not in the sequence since sqrt(8) - (sqrt(1) + sqrt(3)) = 0.09637 ... which again is not an improvement over a(5);

%e 9 is not in the sequence since sqrt(9) - sqrt(8) = 0.17157 ... which is not an improvement of a(5);

%e a(7) is 10 because sqrt(10) - (sqrt(2) + sqrt(3)) = 0.01601 ... ;

%e a(8) is 12 because sqrt(12) - (sqrt(1) + sqrt(6)) = 0.01461 ... ; etc.

%Y Cf. A045880, A333987, A337210.

%K nonn,more

%O 1,2

%A _Robert G. Wilson v_, Aug 19 2020

%E a(24) corrected by _Jinyuan Wang_, Aug 23 2020

%E Title improved, a(26) corrected and a(31)-a(34) from _Sean A. Irvine_, Mar 23 2021