A287639 Lexicographically earliest sequence of distinct positive terms such that the sum of two consecutive terms has Hamming weight >= 10.

1, 1022, 513, 510, 1025, 766, 257, 1278, 641, 382, 1153, 638, 385, 1150, 769, 254, 1281, 702, 321, 1214, 577, 446, 1089, 830, 193, 1342, 449, 574, 961, 62, 1473, 318, 705, 1086, 833, 190, 1345, 670, 353, 1182, 609, 414, 1121, 798, 225, 1310, 481, 542, 993, 30

Offset

1,2

Comments

Conjecturally, this is a permutation of the natural numbers.

This sequence has connections with A288139: here we have a lower bound, there an upper bound, on the Hamming weight of the sum of two consecutive terms.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..8192

Rémy Sigrist, PARI program for A287639

Example

The first terms, alongside a(n)+a(n+1) in binary and its Hamming weight are:
n       a(n)    a(n)+a(n+1)       Hamming weight
--      ----    -----------       --------------
1       1        1111111111       10
2       1022    10111111111       10
3       513      1111111111       10
4       510     10111111111       10
5       1025    11011111111       10
6       766      1111111111       10
7       257     10111111111       10
8       1278    11101111111       10
9       641      1111111111       10
10      382     10111111111       10
11      1153    11011111111       10
12      638      1111111111       10
13      385     10111111111       10
14      1150    11101111111       10
15      769      1111111111       10
16      254     10111111111       10
17      1281    11110111111       10
18      702      1111111111       10
19      321     10111111111       10
20      1214    11011111111       10

Crossrefs

Cf. A000120, A288139.

Sequence in context: A020388 A362361 A306596 * A261676 A165097 A165101

Adjacent sequences: A287636 A287637 A287638 * A287640 A287641 A287642

Keyword

nonn,look,base

Author

Rémy Sigrist, Jun 17 2017

Status

approved