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 A005488 M2528 #24 May 05 2022 08:08:41
%S A005488 0,1,3,6,9,13,18,24,29
%N A005488 Maximal number of edges in a b^{hat} graceful graph with n nodes.
%C A005488 A graph with e edges is 'b^{hat} graceful' if its nodes can be labeled with distinct nonnegative integers so that, if each edge is labeled with the absolute difference between the labels of its endpoints, then the e edges have the distinct labels 1, 2, ..., e.
%C A005488 Equivalently, maximum m for which there's a difference basis with respect to m with n elements. A 'difference basis w.r.t. m' is a set of integers such that every integer from 1 to m is a difference between two elements of the set.
%C A005488 Miller's paper gives these lower bounds for the 11 terms from a(9) to a(19): 29,37,45,51,61,70,79,93,101,113,127. (Bermond's paper gives these as exact values, but quotes Miller as their source.)
%D A005488 J.-C. Bermond, Graceful graphs, radio antennae and French windmills, pp. 18-37 of R. J. Wilson, editor, Graph Theory and Combinatorics. Pitman, London, 1978.
%D A005488 R. K. Guy, Unsolved Problems in Number Theory, Sect. C10.
%D A005488 J. C. P. Miller, Difference bases: Three problems in additive number theory, pp. 299-322 of A. O. L. Atkin and B. J. Birch, editors, Computers in Number Theory. Academic Press, NY, 1971.
%D A005488 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005488 J. Leech, <a href="https://doi.org/10.1112/jlms/s1-31.2.160">On the representation of 1, 2, ..., n by differences</a>, J. Lond. Math. Soc. 31 (1956), 160-169.
%e A005488 a(7)=18: Label the 7 nodes 0,6,9,10,17,22,24 and include all edges except those from 0 to 22, from 0 to 24 and from 17 to 24. {0,6,9,10,17,22,24} is a difference basis w.r.t. 18.
%Y A005488 Cf. A004137, A007187, A239308.
%K A005488 nonn,more
%O A005488 1,3
%A A005488 _N. J. A. Sloane_, _Simon Plouffe_
%E A005488 Edited by _Dean Hickerson_, Jan 26 2003
%E A005488 a(9) from _J. Stauduhar_, May 04 2022