A291041 The arithmetic function uhat(n,7,4).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 7, 13, 8, 13, 9, 13, 10, 7, 11, 13, 8, 13, 13, 9, 7, 13, 10, 13, 8, 11, 13, 7, 9, 13, 13, 13, 8, 13, 7, 13, 11, 9, 13, 13, 8, 7, 10, 13, 13, 13, 9, 11, 7, 13, 13, 13, 10, 13, 13, 7, 8, 13, 11, 13, 13, 13, 7

Offset: 1

Author

Robert Price, Aug 16 2017

Keywords

• nonn

Comments

The sequence appears to be equal to uhat(n,7,3), at least to 10000 terms.

Links

• Bela Bajnok, Additive Combinatorics: A Menu of Research Problems, arXiv:1705.07444 [math.NT], May 2017. See Table in Section 1.6.4.

Crossrefs

Cf. A289435, A289436, A289437, A289438, A289439, A289440, A289441.

Programs

Mathematica

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, 7, 4], {n, 1, 70}]