A109022 Integers with mutual residues of 2 or more.

3, 5, 8, 14, 23, 38, 44, 53, 59, 62, 68, 74, 83, 122, 134, 143, 158, 164, 173, 179, 188, 194, 203, 218, 227, 242, 263, 278, 284, 293, 302, 314, 338, 362, 374, 383, 398, 404, 422, 428, 443, 452, 458, 467, 479, 482, 503, 509, 524, 539, 542, 548, 554, 563, 578

Offset: 1

Author

Seppo Mustonen, Aug 18 2005

Keywords

• nonn

Comments

This is the special case k=2 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 and k=1 prime numbers A000040.

Examples

			The fourth term is 14 since mod(9,3)=0, mod(10,3)=1, mod(11,5)=1,
mod(12,3)=0, mod(13,3)=1 but mod(14,3)=2, mod(14,5)=4, mod(14,8)=6.
		

Links

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

Crossrefs

Cf. A109328-A109335.

Programs

Maple

res_seq:=proc(a::array(1,nonnegint),k,n::nonnegint) local i,j,m,f; a[1]:=k+1; for i from 2 to n do m:=a[i-1]+1; f:=1; while f=1 do j:=1; while j=k do j:=j+1; od; if j=i then a[i]:=m; f:=0; else m:=m+1; fi; od; od; end; a:=array(1..57,[]); res_seq(a,2,57); print(a);

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[2, 57] (* Jean-François Alcover, Oct 05 2022, after Maple code *)