A006998 Partitioning integers to avoid arithmetic progressions of length 3.

0, 1, 2, 4, 6, 8, 12, 14, 16, 24, 26, 28, 32, 40, 48, 52, 54, 56, 64, 72, 80, 96, 100, 104, 108, 110, 112, 128, 136, 144, 160, 176, 192, 200, 204, 208, 216, 218, 220, 224, 240, 256, 272, 280, 288, 320, 336, 352, 384, 392, 400, 408, 412, 416, 432, 434, 436, 440

Offset: 0

Author

N. J. A. Sloane, James Propp

Keywords

• nonn
• look

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Joseph Gerver, James Propp and Jamie Simpson, Greedily partitioning the natural numbers into sets free of arithmetic progressions Proc. Amer. Math. Soc., Vol. 102, No. 3 (1988), 765-772.
• James Propp and N. J. A. Sloane, Email, March 1994

Crossrefs

Cf. A006997, A006999.

Programs

PARI

for (n=1, #a=vector(58), print1 (a[n]=if (n<=2, n-1, a[1+((2*n-2)\3)]+a[1+((2*n-1)\3)])", ")) \\ Rémy Sigrist, Jun 10 2021

Formula

a(n) = a([ 2n/3 ]) + a([ (2n+1)/3 ]).

Extensions

More terms from Rémy Sigrist, Jun 10 2021