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 A092482 Sequence contains no 3-term arithmetic progression, other than its initial terms 1,2,3. 14
 1, 2, 3, 6, 7, 14, 15, 17, 18, 36, 37, 39, 40, 45, 46, 48, 49, 98, 99, 101, 102, 107, 108, 110, 111, 125, 126, 128, 129, 134, 135, 137, 138, 276, 277, 279, 280, 285, 286, 288, 289, 303, 304, 306, 307, 312, 313, 315, 316, 357, 358, 360, 361, 366, 367, 369, 370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(1)=1, a(2)=2, a(3)=3; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression, except for the first triple (1,2,3). LINKS David A. Corneth, Table of n, a(n) for n = 1..8193 (first 512 terms by Jean-François Alcover) Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence. FORMULA For n>2, a(n+2) = 1 + 2^[log2(n)] + sum[k=1, n, (3^A007814(n)+1)/2] = 1 + A053644(n) + A005836(n) (conjectured and checked up to n=512). MATHEMATICA a[n_] := a[n] = If[n < 4, n, For[k = a[n - 1] + 1, True, k++, sp = SequencePosition[Append[Array[a, n - 1], k], {x_, ___, y_, ___, z_} /; y - x == z - y, 2]; If[sp == {{1, 3}}, Return[k]]]]; Table[Print[n, " ", a[n]]; a[n], {n, 1, 512}] (* Comparing with data from conjectured formula: *) b[n_] := If[n < 4, n, 1 + 2^(Length[id = IntegerDigits[n - 2, 2]] - 1) + FromDigits[id, 3]]; Table[b[n], {n, 1, 512}] (* Jean-François Alcover, Jan 15 2019 *) (* Second [much faster] program: *) upto[m_] := Module[{n, v, i, j}, n = Max[m, 3]; v = Table[1, {n}]; For[i = 3, i <= n-1, i++, If[v[[i]] == 1, For[j = Max[1, 2i-n], j <= Min[2n-i, i-1], j++, If[v[[j]] == 1, v[[2i-j]] = 0]]]]; Position[v, 1] // Flatten]; upto[12000] (* Jean-François Alcover, Jan 16 2019, after David A. Corneth *) PROG (PARI) upto(n) = n=max(n, 3); v=vector(n, i, 1); for(i=3, n-1, if(v[i]==1, for(j = max(1, 2*i-n), min(2*n-i, i-1), c=2*i - j; if(v[j]==1, v[2*i-j]=0; )))); select(x -> x==1, v, 1) \\ David A. Corneth, Jan 15 2019 CROSSREFS Cf. A004793, A033157. Sequence in context: A309815 A256800 A172105 * A147303 A075427 A066880 Adjacent sequences:  A092479 A092480 A092481 * A092483 A092484 A092485 KEYWORD nonn AUTHOR Ralf Stephan, Apr 04 2004 EXTENSIONS Name clarified by Charles R Greathouse IV, Jan 30 2014 STATUS approved

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)