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

1,2

Comments

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

Links

Table of n, a(n) for n=1..70.

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

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}]

Crossrefs

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

Sequence in context: A268982 A278065 A373233 * A291766 A291579 A331300

Adjacent sequences: A291038 A291039 A291040 * A291042 A291043 A291044

Keyword

nonn

Author

Robert Price, Aug 16 2017

Status

approved