A086844 Odd numbers m such that the sequence defined by b(1) = m; for k>1, b(k) = floor((1+sqrt(3))*b(k-1)) contains only odd numbers.

5, 7, 13, 19, 21, 27, 29, 35, 37, 43, 49, 51, 57, 59, 65, 67, 71, 73, 79, 81, 87, 89, 95, 97, 101, 103, 109, 111, 117, 119, 125, 131, 133, 139, 141, 147, 149, 155, 161, 163, 169, 171, 177, 179, 183, 185, 191, 193, 199, 201, 207, 213, 215, 221, 223, 229, 231, 237

Offset

1,1

Comments

Conjecture: let r(z)= (1/2) *(z+sqrt(z^2+4*z)), for any integral z>=1. Then the sequence a(n)-4n (where a(n) is the sequence of odd numbers m such that the sequence defined by b(1) = m; for k>1, b(k) = floor(r(z)*b(k-1)) contains only odd numbers) becomes ultimately periodic. Benoit Cloitre, Aug 10 2003

Links

Table of n, a(n) for n=1..58.

Formula

Observation: a(n+1)-a(n) = 2, 4 or 6 for every n, a(n)=4n+O(1) and more precisely it seems that abs(a(n)-4n)<=9. Is the sequence a(n)-4n ultimately periodic ? Benoit Cloitre, Aug 10 2003

Example

For m = 5 we get 5, 13, 35, 95, 259, 707, 1931, 5275, 14411, 39371, ... (cf. A057960).

Crossrefs

Cf. A086843.

Sequence in context: A336581 A248920 A314325 * A109269 A216752 A216740

Adjacent sequences: A086841 A086842 A086843 * A086845 A086846 A086847

Keyword

nonn

Author

Philippe Deléham, Aug 09 2003

Status

approved