A033158 Begins with (1, 5); avoids 3-term arithmetic progressions.

1, 5, 6, 8, 12, 13, 17, 24, 27, 32, 34, 38, 39, 45, 50, 57, 74, 79, 81, 86, 96, 100, 107, 125, 129, 132, 137, 144, 170, 189, 198, 204, 221, 222, 227, 228, 239, 248, 260, 270, 277, 285, 288, 303, 309, 311, 314, 320, 338, 386, 393, 398, 423, 435, 456, 467, 471, 492, 494, 500

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

References

• Iacobescu, F. 'Smarandache Partition Type and Other Sequences.' Bull. Pure Appl. Sci. 16E, 237-240, 1997.
• H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 170-183.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2000
• Eric Weisstein's World of Mathematics, Nonarithmetic Progression Sequence

Crossrefs

Equals A005487(n-1)+1.

Programs

Mathematica

ss[s1_, M_] := Module[{n, chvec, swi, p, s2, i, j, t1, mmm}, t1 = Length[s1]; mmm = 1000; s2 = Table[s1, {t1 + M}] // Flatten; chvec = Array[0 &, mmm]; For[i = 1, i <= t1, i++, chvec[[s2[[i]]]] = 1]; (* get n-th term *) For[n = t1 + 1, n <= t1 + M, n++, (* try i as next term *) For[i = s2[[n - 1]] + 1, i <= mmm, i++, swi = -1; (* test against j-th term *) For[j = 1, j <= n - 2, j++, p = s2[[n - j]]; If[2*p - i < 0, Break[]]; If[chvec[[2*p - i]] == 1, swi = 1; Break[]]]; If[swi == -1, s2[[n]] = i; chvec[[i]] = 1; Break[]]]; If[swi == 1, Print["Error, no solution at n = ", n]]]; Table[s2[[i]], {i, 1, t1 + M}]]; A033158 = ss[{0, 4}, 80] + 1 (* Jean-François Alcover, Oct 08 2013, after Maple program in A185256 *)