A164889 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

1, 5, 10, 14, 15, 17, 24, 28, 32, 27, 40, 34, 42, 49, 39, 48, 61, 53, 56, 65, 66, 60, 74, 76, 67, 83, 79, 88, 43, 93, 103, 86, 98, 102, 110, 115, 119, 99, 127, 114, 128, 90, 138, 111, 122, 139, 141, 152, 140, 121, 147, 149, 158, 168, 159, 146, 176, 162, 173, 177, 157

Offset

1,2

Comments

It appears that the four sequences include every positive integer except 6, 8, 12, 21, and 33.

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.)

Links

Table of n, a(n) for n=1..61.

Prog

(PARI) al(n) = {local(u, r); u=vector(6*n); r=vector(n);
for(i=1, n, for(k=1, 4*i,
if(!u[k]&&!u[k+i]&&!u[k+2*i]&&!u[k+3*i], r[i]=k;
u[k]=u[k+i]=u[k+2*i]=u[k+3*i]=1; break)));
r}

Crossrefs

Cf. A164888.

Sequence in context: A317966 A119139 A313451 * A173553 A226153 A275991

Adjacent sequences: A164886 A164887 A164888 * A164890 A164891 A164892

Keyword

nonn

Author

Franklin T. Adams-Watters, Sep 21 2009

Status

approved