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A233249 a(1)=0; let, for k>=1, prime(k) map to  10...0 with k-1 zeros and prime(k)*prime(m) map to concatenation in binary of 2^(k-1) and 2^(m-1). Let, for n>=2, prime power factorization of n is mapped to r(n). a(n) is the term in A114994 which is c-equivalent to r(n) (see there our comment). 7
0, 1, 2, 3, 4, 5, 8, 7, 10, 9, 16, 11, 32, 17, 18, 15, 64, 21, 128, 19, 34, 33, 256, 23, 36, 65, 42, 35, 512, 37, 1024, 31, 66, 129, 68, 43, 2048, 257, 130, 39, 4096, 69, 8192, 67, 74, 513, 16384, 47, 136, 73, 258, 131, 32768, 85, 132, 71, 514, 1025, 65536, 75 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Let (10...0)_i (i>=0) denote 2^i in binary. Under (10...0)_i^k we understand a concatenation of (10...0)_i k times.

If n=prod {i=1,...,m}p_i^t_i is prime power factorization of n, then in the name r(n)=concatenation{i=1,...,m} ((10...0_(i-1)^t_i).

Numbers q and s are called c-equivalent, if their binary expansions contain the same set of parts of the form 10...0. For example, 14=(1)(1)(10)~(10)(1)(1)=11.

Conversely, if n~n_1, such that n_1 is in A114994 and has c-factorization: n_1= concatenation{i=m,...,0} ((10...0)_i^t_i), one can consider "converse" sequence {s(n)}, where s(n)=prod {i=m,...,0}p_(i+1)^t_i.

For example, for n=22, n_1=21=((10)^2)(1), and s(22)=3^2*2=18.

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..2500

EXAMPLE

n=10=2*5 is mapped to (1)(100)~(100)(1). Since 9 is in A114994, then a(10)=9.

CROSSREFS

Cf. A114994.

Sequence in context: A245822 A069797 A158979 * A330573 A309369 A091893

Adjacent sequences:  A233246 A233247 A233248 * A233250 A233251 A233252

KEYWORD

nonn,base,look

AUTHOR

Vladimir Shevelev, Dec 06 2013

EXTENSIONS

More terms from Peter J. C. Moses, Dec 07 2013

STATUS

approved

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Last modified February 18 02:57 EST 2020. Contains 332006 sequences. (Running on oeis4.)