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A291567
The arithmetic function uhat(n,5,2).
0
1, 2, 3, 4, 5, 6, 7, 7, 7, 5, 7, 6, 7, 7, 5, 7, 7, 6, 7, 5, 7, 7, 7, 6, 5, 7, 7, 7, 7, 5, 7, 7, 7, 7, 5, 6, 7, 7, 7, 5, 7, 6, 7, 7, 5, 7, 7, 6, 7, 5, 7, 7, 7, 6, 5, 7, 7, 7, 7, 5, 7, 7, 7, 7, 5, 6, 7, 7, 7, 5
OFFSET
1,2
COMMENTS
The sequence appears to be equal to uhat(n,5,3), 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.
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, 5, 2], {n, 1, 70}]
KEYWORD
nonn
AUTHOR
Robert Price, Aug 26 2017
STATUS
approved