A291512 The arithmetic function uhat(n,2,7).

-34, -34, -34, -34, -34, -34, -34, -34, -36, -40, -44, -48, -52, -56, -60, -64, -68, -72, -76, -80, -84, -88, -92, -96, -100, -104, -108, -112, -116, -120, -124, -128, -132, -136, -140, -144, -148, -152, -156, -160, -164, -168, -172, -176, -180, -184, -188, -192, -196, -200, -204, -208, -212, -216, -220, -224, -228, -232, -236, -240, -244, -248, -252, -256, -260, -264, -268, -272, -276, -280

Offset

1,1

Comments

Appears to decrement by 4 for each successive term after a(9) = -36. - Chai Wah Wu, Sep 12 2018

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, 2, 7], {n, 1, 70}]

Crossrefs

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

Sequence in context: A361759 A104685 A204773 * A165855 A318148 A271984

Adjacent sequences: A291509 A291510 A291511 * A291513 A291514 A291515

Keyword

sign

Author

Robert Price, Aug 25 2017

Status

approved