

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



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
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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^37x^216x6. (This polynomial is obtained by solving 1/x+1/(x+1)+1/(x+2)+1/(x+3) = 1.)


LINKS



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



KEYWORD

nonn


AUTHOR



STATUS

approved



