A366031 - OEIS

A366031

Square array A(n, k), n, k >= 0, read and filled by upwards antidiagonals the greedy way with distinct nonnegative integers such that the binary expansions of any two distinct terms in the same row or column or antidiagonal have no common 1's.

0, 1, 2, 4, 8, 16, 10, 17, 32, 64, 48, 68, 128, 256, 9, 192, 512, 257, 34, 20, 1024, 768, 1056, 6, 144, 2048, 4096, 8192, 3072, 4224, 520, 8193, 16384, 320, 32768, 36, 12288, 16640, 1088, 2052, 32896, 544, 65536, 131072, 262144, 49152, 67584, 135168, 262152, 258, 524288, 1048576, 1536, 8256, 2097152

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

This sequence is a variant of A366030; here we avoid common 1's in binary expansions, there common prime factors.

All the powers of 2 appear in the sequence, in ascending order.

For any k >= 0, the first term of the sequence whose binary expansion contains 2^k is 2^k.

Will every nonnegative integer appear in the sequence?

LINKS

Table of n, a(n) for n=0..54.

Rémy Sigrist, Colored representation of the array for n, k <= 673 (grayish pixels correspond to powers of 2)

Rémy Sigrist, PARI program

EXAMPLE

Array A(n, k) begins:

n\k| 1 2 3 4 5 6 7 8

---+-----------------------------------------------------------------

1| 0 2 16 64 9 1024 8192 36

2| 1 8 32 256 20 4096 32768 131072

3| 4 17 128 34 2048 320 65536 1536

4| 10 68 257 144 16384 544 1048576 6144

5| 48 512 6 8193 32896 524288 72 4194560

6| 192 1056 520 2052 258 2097153 20480 32784

7| 768 4224 1088 262152 1048608 18 2049 67117056

8| 3072 16640 135168 33280 65600 12 50 129

PROG

(PARI) See Links section.

CROSSREFS

Cf. A366030.

Sequence in context: A277846 A277845 A277858 * A167421 A020954 A070347

Adjacent sequences: A366028 A366029 A366030 * A366032 A366033 A366034

KEYWORD

nonn,base,tabl

AUTHOR

Rémy Sigrist, Sep 26 2023

STATUS

approved