|
%I #4 Mar 11 2018 17:17:21
%S 5,9,10,11,13,17,18,19,20,21,22,23,25,26,27,29,33,34,35,36,37,38,39,
%T 40,41,42,43,44,45,46,47,49,50,52,53,54,55,57,58,59,61,65,66,67,68,69,
%U 70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89
%N Positive numbers k with two consecutive ones in the binary representation of 1/k.
%C Equivalently, these are the numbers k such that A300655(k) > 1.
%C Equivalently, these are the numbers k such that A300653(k, 3) = 3.
%C If n belongs to this sequence then 2*n belongs to this sequence.
%C This sequence has similarities with A004780; here 1/k has two consecutive ones in binary, there k has two consecutive ones in binary.
%C See A300630 for the complementary sequence.
%e The first terms, alongside the binary representation of 1/a(n), are:
%e n a(n) bin(1/a(n)) with repeating digits in parentheses
%e -- ---- ------------------------------------------------
%e 1 5 0.(0011)
%e 2 9 0.(0001110)
%e 3 10 0.0(0011)
%e 4 11 0.(0001011101)
%e 5 13 0.0(00100111011)
%e 6 17 0.(00001111)
%e 7 18 0.0(000111)
%e 8 19 0.(000011010111100101)
%e 9 20 0.00(0011)
%e 10 21 0.(000011)
%o (PARI) is(n) = my (f=1/max(2, n), s=Set()); while (!setsearch(s, f), if (floor(f*4)==3, return (1), s=setunion(s, Set(f)); f=frac(f*2))); return (0)
%Y Cf. A004780, A300653, A300655, A300630 (complement).
%K nonn,base
%O 1,1
%A _Rémy Sigrist_, Mar 11 2018
|
