

A291041


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


3



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
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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: A043273 A268982 A278065 * A291766 A291579 A331300
Adjacent sequences: A291038 A291039 A291040 * A291042 A291043 A291044


KEYWORD

nonn


AUTHOR

Robert Price, Aug 16 2017


STATUS

approved



