|
%I #2 Mar 30 2012 17:35:24
%S 1,5,10,14,15,17,24,28,32,27,40,34,42,49,39,48,61,53,56,65,66,60,74,
%T 76,67,83,79,88,43,93,103,86,98,102,110,115,119,99,127,114,128,90,138,
%U 111,122,139,141,152,140,121,147,149,158,168,159,146,176,162,173,177,157
%N Smallest positive integer for each n such that the sequences a(n), a(n)+n, a(n)+2n, and a(n)+3n have no repeated terms
%C It appears that the four sequences include every positive integer except 6, 8, 12, 21, and 33.
%C It appears that the sequence is asymptotic to c*n, where c = 2.8038... is the positive root of x^4+2x^3-7x^2-16x-6. (This polynomial is obtained by solving 1/x+1/(x+1)+1/(x+2)+1/(x+3) = 1.)
%o (PARI) al(n) = {local(u, r); u=vector(6*n);r=vector(n);
%o for(i=1,n,for(k=1,4*i,
%o if(!u[k]&&!u[k+i]&&!u[k+2*i]&&!u[k+3*i],r[i]=k;
%o u[k]=u[k+i]=u[k+2*i]=u[k+3*i]=1;break)));
%o r}
%Y Cf. A164888.
%K nonn
%O 1,2
%A _Franklin T. Adams-Watters_, Sep 21 2009
|
