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A328282
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a(n) is the least k such that A175930(k) = n.
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0
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1, 3, 2, 15, 6, 4, 5, 255, 30, 12, 13, 16, 9, 11, 10, 65535, 510, 60, 61, 48, 25, 27, 26, 256, 33, 19, 18, 47, 22, 20, 21, 4294967295, 131070, 1020, 1021, 240, 121, 123, 122, 768, 97, 51, 50, 111, 54, 52, 53, 65536, 513, 67, 66, 79, 38, 36, 37, 767, 94, 44, 45
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OFFSET
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1,2
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COMMENTS
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To compute a(n):
- the binary representation of n has k = A000120(n) one bits,
- the binary representation of a(n) has k runs of consecutive equal bits,
- the length of the i-th run in a(n) has length 2^z where z is the number of zeros immediately following the i-th one bit in the binary representation of n,
- this division into sections starting with ones in n or corresponding to a run in a(n) is materialized by slashes in the example section.
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LINKS
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FORMULA
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a(n) <= 2^n-1 with equality iff n is a power of 2.
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EXAMPLE
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The first terms, alongside the binary representation of n and of a(n) with peer sections separated by slashes, are:
n a(n) bin(n) bin(a(n))
-- ----- ------- ----------------
1 1 1 1
2 3 10 11
3 2 1/1 1/0
4 15 100 1111
5 6 10/1 11/0
6 4 1/10 1/00
7 5 1/1/1 1/0/1
8 255 1000 11111111
9 30 100/1 1111/0
10 12 10/10 11/00
11 13 10/1/1 11/0/1
12 16 1/100 1/0000
13 9 1/10/1 1/00/1
14 11 1/1/10 1/0/11
15 10 1/1/1/1 1/0/1/0
16 65535 10000 1111111111111111
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PROG
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(PARI) a(n)={ my (r=[], l, v=0); while (n, r=concat(l=1+valuation(n, 2), r); n \= 2^l); for (i=1, #r, v *= 2^2^(r[i]-1); if (i%2, v += 2^2^(r[i]-1)-1)); v }
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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