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A005487
Starts 0, 4 and contains no 3-term arithmetic progression.
(Formerly M3243)
12
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
OFFSET
0,2
COMMENTS
This is what would now be called the Stanley Sequence S(0,4). See A185256.
REFERENCES
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).
LINKS
P. Erdős, V. Lev, G. Rauzy, C. Sandor, and 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.
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}] ]; ss[{0, 4}, 80] (* Jean-François Alcover, Sep 10 2013, translated from Maple program given in A185256 *)
PROG
(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
CROSSREFS
Equals A033158(n+1)-1. Cf. A185256.
Sequence in context: A344157 A047375 A358805 * A291741 A084087 A175903
KEYWORD
nonn,nice
EXTENSIONS
Name clarified by Charles R Greathouse IV, Jan 30 2014
STATUS
approved