|
Search: id:A081090
|
|
| |
|
| 0, 2, 5, 52, 13525, 9512132552, 1223751003414213892335125, 14245051228051734585272181044575005954679284643762013257552, 248325370258716902160296047400250648328172652961260867788216996480602703989843022661944797399026809280848253678733938880761766091159445263125
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
log(a(n+1))/log(a(n)) -> 1+sqrt(2). The 8-th term has 59 digits, while the 9-th term has 141 digits.
sum(n>0, a(n)/a(n+1) ) = 1/2; the ratio of the terms a(n+1)/a(n), for n>1, form the convergents of the continued fraction series described by A081088; thus a(n+1) = A081088(n)*a(n) + a(n-1), for n>1. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2003
|
|
FORMULA
|
a(n) = a(n-2)*(a(n-1)^2 + 1) for n>3, with a(1)=0, a(2)=2, a(3)=5. Also, a(n)*a(n-1) = A081088(n) for n>2, a(n) = a(n-2)*A081089(n-1) for n>2.
|
|
CROSSREFS
|
Cf. A081086, A081088, A081089.
Adjacent sequences: A081087 A081088 A081089 this_sequence A081091 A081092 A081093
Sequence in context: A102011 A004098 A005114 this_sequence A071880 A071882 A081482
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Hans Havermann (pxp(AT)rogers.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2003
|
|
|
Search completed in 0.002 seconds
|
