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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}.

%I A337211 #24 Mar 23 2021 21:33:37
%S A337211 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 A337211 184,226,264,269,299,419,426,505,545
%N 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}.
%C A337211 This sequence is the original definition of A045880.
%H A337211 Sean A. Irvine, <a href="/A337211/b337211.txt">Table of n, a(n) for n = 1..34</a>
%H A337211 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a337/A337211.java">Java program</a> (github)
%e A337211 a(1) is 1 since sqrt(1) - sqrt(0)                            = 1.00000 ... ;
%e A337211 a(2) is 2 since sqrt(2) - sqrt(1)                            = 0.41421 ...  which is an improvement over a(0);
%e A337211 a(3) is 3 since sqrt(3) - sqrt(2)                            = 0.31783 ... ;
%e A337211 a(4) is 4 since sqrt(4) - sqrt(3)                            = 0.26794 ... ;
%e A337211 a(5) is 5 since sqrt(5) - sqrt(4)                            = 0.23606 ... ;
%e A337211 a(6) is 6 since sqrt(6) - (sqrt(1) + sqrt(2))                = 0.03527 ... ;
%e A337211 7 is not in the sequence since sqrt(7) -  sqrt(6)            = 0.19626 ... which is not an improvement of a(5);
%e A337211 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 A337211 9 is not in the sequence since sqrt(9) - sqrt(8)             = 0.17157 ... which is not an improvement of a(5);
%e A337211 a(7) is 10 because sqrt(10) - (sqrt(2) + sqrt(3))            = 0.01601 ... ;
%e A337211 a(8) is 12 because sqrt(12) - (sqrt(1) + sqrt(6))            = 0.01461 ... ; etc.
%Y A337211 Cf. A045880, A333987, A337210.
%K A337211 nonn,more
%O A337211 1,2
%A A337211 _Robert G. Wilson v_, Aug 19 2020
%E A337211 a(24) corrected by _Jinyuan Wang_, Aug 23 2020
%E A337211 Title improved, a(26) corrected and a(31)-a(34) from _Sean A. Irvine_, Mar 23 2021