A109328 Integers with mutual residues of 3 or more.

4, 7, 11, 19, 27, 31, 47, 75, 87, 103, 131, 139, 159, 179, 195, 215, 223, 251, 291, 307, 327, 335, 339, 347, 355, 367, 383, 411, 531, 535, 543, 579, 599, 635, 643, 663, 691, 699, 719, 747, 831, 843, 851, 867, 879, 887, 907, 943, 1011, 1039, 1095, 1119, 1139

Offset: 1

Author

Seppo Mustonen, Aug 23 2005

Keywords

• nonn

Comments

This is the special case k=3 of sequences with mutual k-residues. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))>=k, i=1,...,n-1}. k=0 gives natural numbers A000027, k=1 prime numbers A000040 and k1=2 gives A109022.

Links

• Seppo Mustonen, On integer sequences with mutual k-residues
• Seppo Mustonen, On integer sequences with mutual k-residues [Local copy]

Programs

Mathematica

seq[k_, n_] := Module[{a, i, j, m, f}, a = Table[0, {n}]; a[[1]] = k + 1; For[i = 2, i <= n, i++, m = a[[i - 1]] + 1; f = 1; While[f == 1, j = 1; While[j < i && Mod[m, a[[j]]] >= k, j = j + 1]; If[j == i, a[[i]] = m; f = 0, m = m + 1]]]; a];
seq[3, 53] (* Jean-François Alcover, Oct 05 2022, after Maple code in links *)