A109329 Integers with mutual residues of 4 or more.

5, 9, 14, 24, 34, 79, 89, 94, 124, 134, 149, 214, 229, 259, 304, 329, 349, 419, 439, 454, 484, 494, 509, 584, 629, 654, 664, 679, 709, 719, 724, 734, 764, 789, 809, 824, 834, 844, 904, 934, 944, 959, 1004, 1014, 1084, 1114, 1139, 1174, 1184, 1214, 1229, 1239

Offset: 1

Author

Seppo Mustonen, Aug 23 2005

Keywords

• nonn

Comments

This is the special case k=4 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 k=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[4, 52] (* Jean-François Alcover, Oct 05 2022, after Maple code in links *)