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A332520
Fixed points of A331364.
3
0, 1, 2, 3, 4, 5, 8, 10, 12, 15, 16, 17, 32, 34, 48, 51, 64, 68, 80, 85, 128, 136, 160, 170, 192, 204, 240, 255, 256, 257, 512, 514, 768, 771, 1024, 1028, 1280, 1285, 2048, 2056, 2560, 2570, 3072, 3084, 3840, 3855, 4096, 4112, 4352, 4369, 8192, 8224, 8704
OFFSET
1,3
COMMENTS
These are the numbers with at most one kind of nonzero digit in any base of the form 2^2^k (with k >= 0).
If k belongs to the sequence, then A001196(k) also belongs to the sequence, and conversely.
For any positive term m:
- the number of runs of consecutive 1's in the binary representation of m is a power of 2,
- the runs of consecutive 1's in the binary representation of m have all the same length, a power of 2.
Apparently, for any k >= 0, there are A001316(k) nonzero terms with 1+k binary digits.
EXAMPLE
The first terms, alongside their binary representation, are:
n a(n) bin(a(n))
-- ---- ---------
1 0 0
2 1 1
3 2 10
4 3 11
5 4 100
6 5 101
7 8 1000
8 10 1010
9 12 1100
10 15 1111
11 16 10000
12 17 10001
13 32 100000
14 34 100010
15 48 110000
16 51 110011
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jun 24 2020
STATUS
approved