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A323418 The third greedy 3-free sequence on nonnegative integers. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 17 17:21 EDT 2021. Contains 348065 sequences. (Running on oeis4.)