A323419 The fourth greedy 3-free sequence on nonnegative integers.

21, 22, 24, 25, 48, 49, 51, 52, 57, 58, 60, 61, 102, 103, 105, 106, 129, 130, 132, 133, 138, 139, 141, 142, 165, 166, 168, 169, 264, 265, 267, 268, 291, 292, 294, 295, 300, 301, 303, 304, 345, 346, 348, 349, 372, 373, 375, 376, 381, 382, 384, 385, 408, 409, 411, 412, 489, 490, 492, 493, 750, 751, 753, 754, 777, 778, 780

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. The next iteration produces sequence A323418. The fourth iteration produces this sequence.

When represented in ternary this sequence consists of integers ending in 10, 11, 20 or 21, and there is exactly one digit 2 before that that might be followed by zeros.

Links

Table of n, a(n) for n=1..67.

Crossrefs

Cf. A005836, A074940, A323398, A323418.

Sequence in context: A199934 A335558 A141439 * A333908 A241851 A295747

Adjacent sequences: A323416 A323417 A323418 * A323420 A323421 A323422

Keyword

nonn

Author

Tanya Khovanova and PRIMES STEP Junior, Jan 14 2019

Status

approved