A080605 Golomb's sequence using odd integers.

1, 3, 3, 3, 5, 5, 5, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 21, 21, 21, 21, 21, 21, 21, 21, 21, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 25, 25, 25, 25, 27

Offset

1,2

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Formula

a(n) = phi^(2-phi)*(2*n)^(phi-1)+O(n^(phi-1)/log(n)) where phi is the golden ratio.

Example

Read 1,3,3,3,5,5,5,7,7,7,9,9,9,9,9,11,11,11,11,11, as 1,(3,3,3),(5,5,5),(7,7,7),(9,9,9,9,9),(11,11,11,11,11), count occurrences between 2 parentheses, gives 1,3,3,3,5,5,... which is the sequence itself.

Prog

(PARI) a=[1, 3, 3, 3]; for(n=3, 20, for(i=1, a[n], a=concat(a, 2*n-1))); a

Crossrefs

Cf. A001462, A080606, A080607.

Sequence in context: A200266 A394051 A101290 * A130823 A101435 A373013

Adjacent sequences: A080602 A080603 A080604 * A080606 A080607 A080608

Keyword

nonn

Author

Benoit Cloitre, Feb 25 2003

Extensions

Corrected at the suggestion of Kevin Ryde by Benoit Cloitre, May 31 2012

Status

approved