A291579 The arithmetic function uhat(n,8,2).

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

Offset

1,2

Comments

uhat(8,6) also generates this sequence.

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, 8, 2], {n, 1, 70}]

Crossrefs

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

Sequence in context: A278065 A291041 A291766 * A331300 A274933 A080331

Adjacent sequences: A291576 A291577 A291578 * A291580 A291581 A291582

Keyword

nonn

Author

Robert Price, Aug 26 2017

Status

approved