cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

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

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Author

Tanya Khovanova and PRIMES STEP Junior, Jan 14 2019

Keywords

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.

Crossrefs

Cf. A005836, A074940, A323398, A323419.

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

Original entry on oeis.org

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

Views

Author

Tanya Khovanova and PRIMES STEP Junior, Jan 14 2019

Keywords

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.

Crossrefs

Cf. A005836, A074940, A323398, A323418.
Showing 1-2 of 2 results.

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