A005487 Starts 0, 4 and contains no 3-term arithmetic progression. (Formerly M3243)

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

Chai Wah Wu, Table of n, a(n) for n = 0..10000

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.

Index entries related to non-averaging sequences

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

Adjacent sequences: A005484 A005485 A005486 * A005488 A005489 A005490

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Name clarified by Charles R Greathouse IV, Jan 30 2014

Status

approved