A115516 The mode of the bits of n (using 0 if bimodal).
0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0
Offset: 0
Examples
a(5)=1 because 5 = 101 (binary) and 0 occurs once, but 1 occurs twice, so 1 is the mode. 5 is a member of A044951 (Numbers with no two equally numerous base 2 digits). a(10)=0 because 10 = 1010 (binary), where 0 and 1 each occur twice. As these bits are bimodal, 0 is chosen. 10 is a member of A031443 (Digitally balanced numbers: numbers which in base 2 have the same number of 0's as 1's.).
Links
- Paolo Xausa, Table of n, a(n) for n = 0..10000
Crossrefs
Programs
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Mathematica
Array[Min[Commonest[IntegerDigits[#, 2]]] &, 100, 0] (* Paolo Xausa, May 21 2024 *)
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PARI
{for(n=0,104, b=binary(n); l=length(b); s=sum(m=1,l,b[m]); if(s>l-s, a=1, a=0); print1(a,","))}
Formula
a(A031443(k))=0 for k>=1.
Comments