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 A291520 #13 Jun 11 2025 00:58:27
%S A291520 1,2,3,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,
%T A291520 5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,
%U A291520 5,4
%N A291520 The arithmetic function uhat(n,4,2).
%H A291520 Michael De Vlieger, <a href="/A291520/b291520.txt">Table of n, a(n) for n = 1..10000</a>
%H A291520 Bela Bajnok, <a href="https://arxiv.org/abs/1705.07444">Additive Combinatorics: A Menu of Research Problems</a>, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.4.
%F A291520 Conjectures from _Chai Wah Wu_, Jun 10 2025: (Start)
%F A291520 a(n) = a(n-2) for n > 5.
%F A291520 G.f.: x*(-2*x^4 - 2*x^3 - 2*x^2 - 2*x - 1)/(x^2 - 1). (End)
%t A291520 delta[r_, k_, d_] := If[r < k, (k - r)*r - (d - 1), If[k < r && r < d, (d - r)*(r - k) - (d - 1), If[k == r && r == d, d - 1, 0]]] uhat[n_, m_, h_] := (dx = Divisors[n]; dmin = n; For[i = 1, i ≤ Length[dx], i++, d = dx[[i]]; k = m - d*Ceiling[m/d] + d; r = h - d*Ceiling[h/d] + d; If[h ≤ Min[k, d - 1], dmin = Min[dmin, n, (h*Ceiling[m/d] - h + 1)*d, h*m - h*h + 1], dmin = Min[dmin, n, h*m - h*h + 1 - delta[r, k, d]]]]; dmin) Table[uhat[n, 4, 2], {n, 1, 70}]
%Y A291520 Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.
%K A291520 nonn
%O A291520 1,2
%A A291520 _Robert Price_, Aug 25 2017