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A115517
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The mode of the bits of n (using 1 if bimodal).
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1
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0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 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
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OFFSET
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0,1
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COMMENTS
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If n is a term of A044951, A115516(n) = a(n); otherwise, A115516(n) = 0 and a(n) = 1 (and n is a term of A031443).
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LINKS
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Table of n, a(n) for n=0..104.
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FORMULA
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a(A031443(k))=1 for k>=1.
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EXAMPLE
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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)=1 because 10 = 1010 (binary), where 0 and 1 each occur twice. As these bits are bimodal, 1 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.).
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PROG
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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, ", "))}
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CROSSREFS
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Cf. A115516 (same but use 0 if bimodal), A031443 (n's bits bimodal), A044951 (n's bits unimodal), A115353 (mode of n's decimal digits).
Sequence in context: A075553 A131729 A144609 * A022930 A068344 A161382
Adjacent sequences: A115514 A115515 A115516 * A115518 A115519 A115520
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KEYWORD
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base,nonn
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AUTHOR
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Rick L. Shepherd, Jan 23 2006
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STATUS
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approved
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