A165818 Largest integer coprime to n whose binary representation is a substring of the binary representation of n.

1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 3, 7, 1, 8, 1, 9, 1, 10, 5, 11, 1, 12, 5, 13, 3, 14, 7, 15, 1, 16, 1, 17, 1, 18, 9, 19, 1, 20, 5, 21, 5, 22, 11, 23, 1, 24, 9, 25, 5, 26, 13, 27, 3, 28, 13, 29, 7, 30, 15, 31, 1, 32, 1, 33, 1, 34, 17, 35, 1, 36, 9, 37, 9, 38, 19, 39, 1, 40, 9, 41, 5, 42, 21

Offset

1,5

Links

Table of n, a(n) for n=1..86.

Example

14 in binary is 1110. The integers that, when written in binary, occur as substrings in 1110 are 0, 1, 2 (10 in binary), 3 (11 in binary), 6 (110 in binary), 7 (111 in binary), and 14 (1110 in binary). Of these, 3 is the largest that is coprime to 14. So a(14) = 3.

Prog

(PARI) { a(n) = my(m, b, s); m=0; b=binary(n); for(i=1, #b, for(j=i, #b, s=sum(k=i, j, b[k]*2^(j-k)); if(gcd(s, n)==1&&m<s, m=s) )); m } /* Max Alekseyev, Oct 01 2009 */

Crossrefs

Sequence in context: A090331 A338759 A229994 * A369895 A194746 A198336

Adjacent sequences: A165815 A165816 A165817 * A165819 A165820 A165821

Keyword

base,nonn

Author

Leroy Quet, Sep 28 2009

Extensions

More terms from Max Alekseyev, Oct 01 2009

Status

approved