A072893 Let c(k) be defined as follows: c(1)=1, c(2)=x, c(k+2) = c(k+1)/2 + c(k)/2 if c(k+1) and c(k) have the same parity; c(k+2) = c(k+1) - c(k) otherwise. Sequence gives values of x such that c(k)=1 for any k large enough.

1, 2, 3, 6, 8, 11, 13, 18, 21, 23, 28, 31, 33, 43, 46, 51, 53, 56, 58, 66, 71, 73, 78, 83, 86, 88, 91, 93, 96, 98, 101, 106, 111, 113, 121, 123, 128, 131, 133, 136, 138, 141, 146, 153, 158, 161, 171, 173, 176, 178, 181, 183, 188, 193, 201, 203, 206, 211, 216, 218

Offset

1,2

Comments

Conjectures: (1) Lim n ->infinity a(n)/n = C = 3.5.... (2) For any n > 2, a(n+1)-a(n) = 2, 3, 5, 7, 8 or 10 only. First differences a(n+1)-a(n) for n>2 are 3, 2, 3, 2, 5, 3, 2, 5, 3, 2, 10, 3, 5, 2, 3, 2, 8... (3) If x is not in this sequence, for k large enough, c(k)= -1 or c(k) reaches one of the two cycles {3, 1, 2, -1} or {0, -1, 1, 0, 1, -1}.

Links

Table of n, a(n) for n=1..60.

Example

If x = 6, c(3)=5, c(4)=-1, c(5)=2, c(6)=3, c(7)=1, c(8)=2, c(9)=1, c(10)=-1, c(11)=0, c(12)=1, c(13)=1, c(14)=1, c(15)=1, ... Hence 6 is in the sequence.

Crossrefs

Sequence in context: A099798 A230108 A097383 * A349662 A371002 A127758

Adjacent sequences: A072890 A072891 A072892 * A072894 A072895 A072896

Keyword

easy,nonn

Author

Benoit Cloitre, Jul 29 2002

Status

approved