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A005487
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Starts 0, 4 and contains no 3-term arithmetic progression.
(Formerly M3243)
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11
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0, 4, 5, 7, 11, 12, 16, 23, 26, 31, 33, 37, 38, 44, 49, 56, 73, 78, 80, 85, 95, 99, 106, 124, 128, 131, 136, 143, 169, 188, 197, 203, 220, 221, 226, 227, 238, 247, 259, 269, 276, 284, 287, 302, 308, 310, 313, 319, 337, 385, 392, 397, 422, 434, 455, 466, 470
(list;
graph;
refs;
listen;
history;
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OFFSET
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0,2
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COMMENTS
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This is what would now be called the Stanley Sequence S(0,4). See A185256.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, E10.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Chai Wah Wu, Table of n, a(n) for n = 0..10000
P. Erdos, V. Lev, G. Rauzy, C. Sandor, A. Sarkozy, Greedy algorithm, arithmetic progressions, subset sums and divisibility, Discrete Mathematics 200 (1999), pp. 119-135.
R. A. Moy and D. Rolnick, Novel structures in Stanley sequences, arXiv:1502.06013 [math.CO], 2015.
R. A. Moy and D. Rolnick, Novel structures in Stanley sequences, Discrete Math., 339 (2016), 689-698.
A. M. Odlyzko and R. P. Stanley, Some curious sequences constructed with the greedy algorithm, 1978
Index entries related to non-averaging sequences
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MATHEMATICA
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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}] ]; ss[{0, 4}, 80] (* Jean-François Alcover, Sep 10 2013, translated from Maple program given in A185256 *)
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PROG
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(Python)
A005487_list = [0, 4]
for i in range(101-2):
n, flag = A005487_list[-1]+1, False
while True:
for j in range(i+1, 0, -1):
m = 2*A005487_list[j]-n
if m in A005487_list:
break
if m < A005487_list[0]:
flag = True
break
else:
A005487_list.append(n)
break
if flag:
A005487_list.append(n)
break
n += 1 # Chai Wah Wu, Jan 05 2016
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CROSSREFS
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Equals A033158(n+1)-1. Cf. A185256.
Sequence in context: A074300 A344157 A047375 * A291741 A084087 A175903
Adjacent sequences: A005484 A005485 A005486 * A005488 A005489 A005490
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Name clarified by Charles R Greathouse IV, Jan 30 2014
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STATUS
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approved
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