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

0,1

Comments

If n is a term of A044951, A115517(n) = a(n); otherwise, A115517(n) = 1 and a(n) = 0 (and n is a term of A031443).

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Formula

a(A031443(k))=0 for k>=1.

Example

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.).

Mathematica

Array[Min[Commonest[IntegerDigits[#, 2]]] &, 100, 0] (* Paolo Xausa, May 21 2024 *)

Prog

(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, ", "))}

Crossrefs

Cf. A115517 (same but use 1 if bimodal), A031443 (n's bits bimodal), A044951 (n's bits unimodal), A115353 (mode of n's decimal digits).

Sequence in context: A288473 A130853 A353810 * A285830 A288741 A341684

Adjacent sequences: A115513 A115514 A115515 * A115517 A115518 A115519

Keyword

base,nonn

Author

Rick L. Shepherd, Jan 23 2006

Status

approved