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 A164888 Smallest positive integer for each n such that the sequences a(n), a(n)+n, and a(n)+2n have no repeated terms. 1
 1, 4, 7, 11, 12, 14, 9, 21, 18, 24, 28, 30, 25, 31, 32, 33, 35, 40, 41, 43, 46, 48, 55, 56, 57, 61, 64, 53, 66, 68, 71, 73, 75, 72, 77, 74, 84, 85, 86, 89, 90, 93, 96, 99, 100, 103, 97, 111, 114, 115, 116, 119, 120, 94, 126, 122, 117, 127, 130, 132, 136, 138, 142, 150, 134 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the a(n)+2n is left out, this definition gives us the lower Wythoff sequence, A000201. It appears that the three sequences include every positive integer except 5. It appears that the sequence is asymptotic to c*n, where c = 2.2143... is the positive root of x^3-4x-2. It appears that a(n) = c*n + O(log(n)); possibly even a(n) = c*n + O(1). (This polynomial is obtained by solving 1/x+1/(x+1)+1/(x+2) = 1.) LINKS EXAMPLE The first term is 1; the sequences start 1; 2; 3. The smallest possible value for a(2) is then 4, giving 1,4; 2,6; and 3,8. a(3) cannot be 5, because a(3)+3 = 8 in the second sequence would then duplicate the 8 in the third sequence. a(3) = 7 works; the sequences to that point are 1,4,7; 2,6,10; 3,8,13. PROG (PARI) al(n) = {local(u, r); u=vector(5*n); r=vector(n); for(i=1, n, for(k=1, 3*i, if(!u[k]&&!u[k+i]&&!u[k+2*i], r[i]=k; u[k]=u[k+i]=u[k+2*i]=1; break))); r} CROSSREFS Cf. A000201, A164889, A005228, A000027. Sequence in context: A032547 A075630 A274341 * A023985 A023979 A319280 Adjacent sequences:  A164885 A164886 A164887 * A164889 A164890 A164891 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Sep 21 2009 STATUS approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)