cp's OEIS Frontend

A330925 For any n >= 0: consider all pairs of numbers (x, y) whose binary representations can be interleaved (or shuffled) to produce the binary representation of n (possibly with leading zeros); a(n) is the greatest possible value of x*y.

%I A330925 #15 Jan 05 2020 14:39:58
%S A330925 0,0,0,1,0,2,2,3,0,4,4,6,4,6,6,9,0,8,8,12,8,12,12,15,8,12,12,18,12,18,
%T A330925 18,21,0,16,16,24,16,24,24,28,16,24,24,30,24,30,30,35,16,24,24,36,24,
%U A330925 36,36,42,24,36,36,42,36,42,42,49,0,32,32,48,32,48,48
%N A330925 For any n >= 0: consider all pairs of numbers (x, y) whose binary representations can be interleaved (or shuffled) to produce the binary representation of n (possibly with leading zeros); a(n) is the greatest possible value of x*y.
%C A330925 Interleaving (or shuffling) two strings means combining all their characters while preserving the order of all characters in individual strings; for example, "12345" is the interleaving of "14" and "235".
%H A330925 Rémy Sigrist, <a href="/A330925/b330925.txt">Table of n, a(n) for n = 0..8192</a>
%H A330925 Rémy Sigrist, <a href="/A330925/a330925.txt">C program for A330925</a>
%H A330925 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A330925 a(n) = 0 iff n is zero or a power of 2.
%F A330925 a(2*n) = 2*a(n).
%e A330925 For n = 5:
%e A330925 - the binary representation of 5 is "101",
%e A330925 - the possible values for (x, y), restricted to x >= y without loss of generality, are:
%e A330925   bin(5)   x  y  x*y
%e A330925   -------  -  -  ---
%e A330925   "101"    5  0    0
%e A330925   "1/01"   1  1    1
%e A330925   "10/1"   2  1    2
%e A330925   "1/0/1"  3  0    0
%e A330925 - hence a(5) = 2.
%o A330925 (C) See Links section.
%Y A330925 Cf. A330955 (x AND y variant), A330958 (x OR y variant), A330959 (x XOR y variant).
%Y A330925 Cf. A330956 (min(x, y) variant), A330957 (max(x, y) variant).
%Y A330925 Cf. A330960 (x + y variant), A330961 (x - y variant).
%Y A330925 Cf. A330962 (x^2 + y^2 variant), A330963 (x^2 - y^2 variant).
%Y A330925 See A327186 for similar sequences where we split the binary representation.
%K A330925 nonn,base
%O A330925 0,6
%A A330925 _Rémy Sigrist_, Jan 03 2020