

A351705


For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the numerator of d(n) = Sum_{k >= 0} b_k * 2^A130472(k). See A351706 for the denominators.


4



0, 1, 1, 3, 2, 3, 5, 7, 1, 5, 3, 7, 9, 13, 11, 15, 4, 5, 9, 11, 6, 7, 13, 15, 17, 21, 19, 23, 25, 29, 27, 31, 1, 9, 5, 13, 17, 25, 21, 29, 3, 11, 7, 15, 19, 27, 23, 31, 33, 41, 37, 45, 49, 57, 53, 61, 35, 43, 39, 47, 51, 59, 55, 63, 8, 9, 17, 19, 10, 11, 21
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OFFSET

0,4


COMMENTS

The function d is a bijection from the nonnegative integers to the nonnegative dyadic rationals satisfying d(A000695(n)) = n for any n >= 0.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8191
Wikipedia, Dyadic rational
Index entries for sequences related to binary expansion of n


FORMULA

a(A000695(n)) = n.
a(2^k) = A072345(k1) for any k > 0.
a(2^k1) = 2^k1 for any k >= 0.
A000120(a(n)) = A000120(n).


EXAMPLE

For n = 13:
 13 = 2^0 + 2^2 + 2^3,
 A130472(0) = 0, A130472(2) = 1, A130472(3) = 2,
 d(13) = 2^0 + 2^1 + 2^2 = 13/4,
 so a(13) = 13.


PROG

(PARI) a(n) = { my (d=0, k); while (n, n=2^k=valuation(n, 2); d+=2^((1)^k*(k+1)\2)); numerator(d) }


CROSSREFS

Cf. A000120, A000695, A072345, A351706, A351785, A351786.
Sequence in context: A347266 A050060 A247829 * A246592 A241816 A243109
Adjacent sequences: A351702 A351703 A351704 * A351706 A351707 A351708


KEYWORD

nonn,base,frac


AUTHOR

Rémy Sigrist, Feb 16 2022


STATUS

approved



