cp's OEIS Frontend

A351706 For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the denominator of d(n) = Sum_{k >= 0} b_k * 2^A130472(k). See A351705 for the numerators.

%I A351706 #16 Feb 23 2022 10:51:03
%S A351706 1,1,2,2,1,1,2,2,4,4,4,4,4,4,4,4,1,1,2,2,1,1,2,2,4,4,4,4,4,4,4,4,8,8,
%T A351706 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,1,1,2,2,
%U A351706 1,1,2,2,4,4,4,4,4,4,4,4,1,1,2,2,1,1,2
%N A351706 For any nonnegative number n with binary expansion Sum_{k >= 0} b_k * 2^k, a(n) is the denominator of d(n) = Sum_{k >= 0} b_k * 2^A130472(k). See A351705 for the numerators.
%C A351706 The function d is a bijection from the nonnegative integers to the nonnegative dyadic rationals satisfying d(A000695(n)) = n for any n >= 0.
%H A351706 Rémy Sigrist, <a href="/A351706/b351706.txt">Table of n, a(n) for n = 0..8191</a>
%H A351706 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dyadic_rational">Dyadic rational</a>
%H A351706 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A351706 a(A000695(n)) = 1.
%F A351706 a(2^k) = A072345(k) for any k >= 0.
%F A351706 a(2^k-1) = A016116(k) for any k >= 0.
%e A351706 For n = 13:
%e A351706 - 13 = 2^0 + 2^2 + 2^3,
%e A351706 - A130472(0) = 0, A130472(2) = 1, A130472(3) = -2,
%e A351706 - d(13) = 2^0 + 2^1 + 2^-2 = 13/4,
%e A351706 - so a(13) = 4.
%o A351706 (PARI) a(n) = { my (d=0, k); while (n, n-=2^k=valuation(n,2); d+=2^((-1)^k*(k+1)\2)); denominator(d) }
%Y A351706 Cf. A000695, A016116, A072345, A351705, A351785, A351786.
%K A351706 nonn,base,frac
%O A351706 0,3
%A A351706 _Rémy Sigrist_, Feb 16 2022