A200322 Related to numbers written in base 2 (see below for definition).

1, 1, 2, 3, 4, 5, 4, 7, 8, 9, 10, 9, 8, 9, 8, 15, 16, 17, 18, 17, 16, 21, 18, 17, 16, 17, 16, 19, 16, 17, 16, 31, 32, 33, 34, 33, 36, 33, 34, 33, 32, 33, 42, 33, 32, 37, 34, 33, 32, 33, 32, 35, 32, 33, 36, 35, 32, 33, 32, 35, 32, 33, 32, 63, 64

Offset

0,3

Comments

Write b(k) as the first k+1 binary digits of n, and write c(k) as the last k+1 binary digits of n, for k=0..m where 2^m <= n < 2^(m+1). Set d(k) = 1 if b(k) = c(k) and d(k) = 0 otherwise. Then d(k) forms the binary digits of a(n): a(n) = Sum_{k=0..m} d(k)*2^k.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..1024

Example

n = 27 (in base 10) = 11011 (in base 2)
b(k) : 1 ; 11; 110; 1101; 11011
c(k) : 1 ; 11; 011; 1011; 11011
d(k) : 1 ; 1; 0; 0; 1
a(27) = 10011 (in base 2) = 19.

Prog

(PARI) {a(n)=local(B, m, b, c, d); B=binary(n); m=#B; d=vector(m); for(k=1, m, b=vector(k, j, B[j]); c=vector(k, j, B[m-k+j]); if(b==c, d[k]=1, d[k]=0)); subst(truncate(Ser(d)), x, 2)}

Crossrefs

Sequence in context: A079867 A273290 A079869 * A361479 A075054 A158366

Adjacent sequences: A200319 A200320 A200321 * A200323 A200324 A200325

Keyword

nonn

Author

Philippe Deléham, Nov 16 2011

Status

approved