A323418 The third greedy 3-free sequence on nonnegative integers.

7, 8, 16, 17, 19, 20, 34, 35, 43, 44, 46, 47, 55, 56, 88, 89, 97, 98, 100, 101, 115, 116, 124, 125, 127, 128, 136, 137, 163, 164, 250, 251, 259, 260, 262, 263, 277, 278, 286, 287, 289, 290, 298, 299, 331, 332, 340, 341, 343, 344, 358, 359, 367, 368, 370, 371, 379, 380, 406, 407, 487, 488, 736, 737, 745, 746, 748, 749

Offset

1,1

Comments

Consider the lexicographically earliest sequence of nonnegative integers that does not contain the arithmetic mean of any pair of terms (such sequences are called 3-free sequences as they do not contain 3-term arithmetic progressions): 0,1,3,4 and so on. This sequence is Stanley sequence S(0,1). Remove numbers in the Stanley sequence from nonnegative integers and repeat the process of finding the next earliest 3-free sequence, which is sequence A323398. We get this sequence on the next iteration.

When represented in ternary this sequence consists of integers ending in 1 or 2, and there is exactly one digit 2 before that that might be followed by zeros.

Links

Table of n, a(n) for n=1..68.

Crossrefs

Cf. A005836, A074940, A323398, A323419.

Sequence in context: A041427 A042755 A093083 * A125195 A099534 A318613

Adjacent sequences: A323415 A323416 A323417 * A323419 A323420 A323421

Keyword

nonn

Author

Tanya Khovanova and PRIMES STEP Junior, Jan 14 2019

Status

approved