A392738 Positions of 0's in A392736.

0, 3, 5, 7, 9, 11, 12, 14, 17, 19, 20, 22, 25, 26, 28, 31, 33, 35, 36, 38, 41, 42, 44, 47, 48, 50, 53, 54, 56, 59, 61, 63, 65, 67, 68, 70, 73, 74, 76, 79, 80, 82, 85, 86, 88, 91, 93, 95, 97, 98, 100, 103, 104, 106, 109, 110, 112, 115, 117, 119, 121, 123, 124

Offset

1,2

Comments

a(n) is the n-th position where the sequence A392736 equals 0. For any balanced binary sequence, the odious and evil enumerators u(n), v(n) satisfy u(n) + v(n) = 4n + 1.

Links

Table of n, a(n) for n=1..63.

Formula

A392737(n) + a(n) = 4n + 1.

Example

a(1) = 0 because A392736 = 0,1,1,0,1,... and the first 0 is at position 0.

Mathematica

M[0] = 0; M[1] = 1; M[n_] := M[n] = Which[Mod[n, 4] == 0, M[Quotient[n, 4]], Mod[n, 4] == 1, 1 - M[Quotient[n, 4]], Mod[n, 4] == 2, M[2*Quotient[n, 4] + 1 - M[Quotient[n, 4]]], True, 1 - M[2*Quotient[n, 4] + 1 - M[Quotient[n, 4]]]]; Select[Range[0, 120], M[#] == 0 &]

Prog

(PARI) M(n) = if(n<2, n, my(q=n\4, r=n%4); if(r==0, M(q), r==1, 1-M(q), r==2, M(2*q+1-M(q)), 1-M(2*q+1-M(q))));
a(n) = my(k=0, c=0); while(c<n, if(M(k)==0, c++); if(c<n, k++)); k;

Crossrefs

Cf. A392736, A392737, A001969 (evil numbers).

Sequence in context: A329827 A182765 A246407 * A151916 A187687 A056617

Adjacent sequences: A392735 A392736 A392737 * A392739 A392740 A392741

Keyword

nonn,easy

Author

John M. Campbell and Benoit Cloitre, Jan 21 2026

Extensions

a(51) onward corrected by Sean A. Irvine, Jan 25 2026

Status

approved