This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A332553 #28 Apr 30 2020 21:03:25 %S A332553 1,2,3,2,3,6,5,3,5,7,8,6,4,10,15,8,9,14,5,7,11,15,9,12,8,6,21,14,15, %T A332553 30,21,11,17,7,24,18,12,15,32,20,21,32,8,15,23,31,27,14,16,12,39,26,9, %U A332553 15,32,19,29,39,40,30,20,42,51,10,33,50,17,23,35 %N A332553 a(n) = n + A082183(n) - A082184(n). %C A332553 Since (by definition) a(n) = n + A082183(n) - A082184(n) = - (n^2 + A082183(n)^2 - A082184(n)^2), this can be described as the distance of (n, A082183(n), A082184(n)) from a Pythagorean triple. Also a(n) > 0 for all n. See the Myers et al. link. - _Bradley Klee_, Feb 19 2020 %C A332553 Comments from _N. J. A. Sloane_, Feb 23 2020: (Start) %C A332553 To study the lowest values taken by a(n), consider the record high values of n/a(n). The data suggests two conjectures. %C A332553 Conjecture 1: The record high values of n/a(n) are j/2 + 1 for j = 2,3,4,5,... and occur at n = j*(j+1)/2 - 1. %C A332553 This would imply: %C A332553 Conjecture 2: Let j = 2,3,4,5,... For 1 <= n < T_j - 1, a(n) > 2*n/(j+2). (End) %H A332553 N. J. A. Sloane, <a href="/A332553/b332553.txt">Table of n, a(n) for n = 2..1000</a> %H A332553 J. S. Myers, R. Schroeppel, S. R. Shannon, N. J. A. Sloane, and P. Zimmermann, <a href="http://arxiv.org/abs/2004.14000">Three Cousins of Recaman's Sequence</a>, arXiv:2004:14000, April 2020. %Y A332553 Cf. A082183, A082184, A332552. %K A332553 nonn %O A332553 2,2 %A A332553 _N. J. A. Sloane_, Feb 21 2020, at the suggestion of _Bradley Klee_