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 A374486 #75 Aug 20 2024 09:08:33 %S A374486 1,2,4,5,6,7,8,9,10,12,13,14,15,16,18,19,20,21,22,24,25,26,27,28,29, %T A374486 30,31,33,37,39,40,42,44,48,50,51,52,53,56,59,62,66,68,70,72,74,77,79, %U A374486 87,91,92,96,97,103,108,112,115,117,120,121,124,130,131,138,148,149,161,164,176,184,185,194,200 %N A374486 Numbers k such that Taxicab(2,j,k) exists for large j. %C A374486 Here Taxicab(2,j,k) denotes the smallest number (if it exists) that is the sum of j perfect squares in exactly k ways. For sufficiently large N, Taxicab(2,j,k) either always exists for j > N or always does not exist for j > N. %C A374486 Conjecture: Infinitely many positive integers are in this sequence, and infinitely many positive integers are not in this sequence. %C A374486 Conjecture: This sequence grows exponentially. Computationally it appears to have asymptotic a(n) = 1.03691*exp(0.594473*n^(1/2)). %D A374486 E. Grosswald. Representations of Integers as Sums of Squares. Springer New York, NY, 1985. %H A374486 Oliver Lippard, <a href="/A374486/b374486.txt">Table of n, a(n) for n = 1..372</a> %H A374486 B. Benfield, O. Lippard, and A. Roy, <a href="https://arxiv.org/abs/2404.08190">End Behavior of Ramanujan's Taxicab Numbers</a>, arXiv:2404.08190 [math.NT], 2024. %e A374486 For k = 3, Taxicab(2,j,3) does not exist for all j > 9, hence 3 is not a member of the sequence. %Y A374486 Cf. A025416, A080673, A295702, A295795 %K A374486 nonn %O A374486 1,2 %A A374486 _Oliver Lippard_ and _Brennan G. Benfield_, Aug 04 2024