A006998 Partitioning integers to avoid arithmetic progressions of length 3. (Formerly M0990)

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

0,3

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

Formula

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

Prog

(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

Crossrefs

Cf. A006997, A006999.

Sequence in context: A331994 A043723 A331681 * A043726 A043730 A043735

Adjacent sequences: A006995 A006996 A006997 * A006999 A007000 A007001

Keyword

nonn,look

Author

N. J. A. Sloane, James Propp

Extensions

More terms from Rémy Sigrist, Jun 10 2021

Status

approved