|
Search: id:A076125
|
|
|
| A076125 |
|
Define r(k) as follows: r(1)=n, r(k+1) = r(k) +(-1)^k*sign(r(k)-k)*k; then abs(r(k)) = n for at least one k>1 (there could be 2 values for k>1). Sequence gives the smallest value of k>1 such that abs(r(k)) = n. |
|
+0
1
|
|
| 2, 4, 9, 8, 8, 25, 12, 12, 29, 16, 16, 37, 20, 20, 61, 24, 24, 57, 28, 28, 65, 32, 32, 129, 36, 36, 85, 40, 40, 93, 44, 44, 129, 48, 48, 113, 52, 52, 121, 56, 56, 165, 60, 60, 141, 64, 64, 149, 68, 68, 265, 72, 72, 169, 76, 76, 177, 80, 80, 233, 84, 84, 197, 88, 88, 205
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
If n=3k+1 or 3k+2, abs(r(x))=n for x=4k+4 and x=8k+1 (first solution only is in the sequence). This was inspired by the Recaman sequence (A005132).
|
|
FORMULA
|
For k>=1, a(3k+1)=a(3k+2)=4k+4; for m>=2, k>=1, a(3^m*k)=3^(m-2)*28*k+1. For a(3^m*k+a) it is more complicate to give a general formula, as examples: a(9k+3)=28k+9; a(9k+6)=36k+25; a(27k+3)=84k+9; a(27k+6)=104k+25; a(27k+9)=84k+29; a(27k+12)=84k+37; a(27k+24)=136k+129. sum(k=1, n, a(k)) is asymptotic to n^2.
|
|
EXAMPLE
|
If r(1)=5: r(8)=5, hence a(5)=8
|
|
CROSSREFS
|
Cf. A005132.
Sequence in context: A055858 A141389 A133757 this_sequence A011033 A033149 A131094
Adjacent sequences: A076122 A076123 A076124 this_sequence A076126 A076127 A076128
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 31 2002
|
|
|
Search completed in 0.002 seconds
|
