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A033158 Begins with (1, 5); avoids 3-term arithmetic progressions. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

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-Fran├žois Alcover, Oct 08 2013, after Maple program in A185256 *)

CROSSREFS

Equals A005487(n-1)+1.

Sequence in context: A048583 A169622 A047321 * A193569 A032721 A105106

Adjacent sequences:  A033155 A033156 A033157 * A033159 A033160 A033161

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 14 13:42 EDT 2021. Contains 345025 sequences. (Running on oeis4.)