

A200322


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


1



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
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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[mk+j]); if(b==c, d[k]=1, d[k]=0)); subst(truncate(Ser(d)), x, 2)}


CROSSREFS

Sequence in context: A079867 A273290 A079869 * A075054 A158366 A335834
Adjacent sequences: A200319 A200320 A200321 * A200323 A200324 A200325


KEYWORD

nonn


AUTHOR

Philippe Deléham, Nov 16 2011


STATUS

approved



