|
Search: id:A010076
|
|
|
| A010076 |
|
a(n) = sum of base 9 digits of a(n-1) + sum of base 9 digits of a(n-2). |
|
+0
13
|
|
| 0, 1, 1, 2, 3, 5, 8, 13, 13, 10, 7, 9, 8, 9, 9, 2, 3, 5, 8, 13, 13, 10, 7, 9, 8, 9, 9, 2, 3, 5, 8, 13, 13, 10, 7, 9, 8, 9, 9, 2, 3, 5, 8, 13, 13, 10, 7, 9, 8, 9, 9, 2, 3, 5, 8, 13, 13, 10, 7, 9, 8, 9, 9, 2, 3, 5, 8, 13, 13, 10, 7, 9, 8, 9, 9
(list; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
The digital sum analogue (in base 9) of the Fibonacci recurrence. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n) and Fib(n)=A000045(n) are congruent modulo 8 which implies that (a(n) mod 8) is equal to (Fib(n) mod 8) = A079344(n). Thus (a(n) mod 8) is periodic with the Pisano period A001175(8)=12. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)==A004090(n) modulo 8 (A004090(n)=digital sum of Fib(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
For general bases p>2, we have the inequality 2<=a(n)<=2p-3 (for n>2). Actually, a(n)<=13=A131319(9) for the base p=9. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
|
|
FORMULA
|
Periodic from n=3 with period 12. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 13 2006
a(n)=a(n-1)+a(n-2)-8*(floor(a(n-1)/9)+floor(a(n-2)/9)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=floor(a(n-1)/9)+floor(a(n-2)/9)+(a(n-1)mod 9)+(a(n-2)mod 9). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=(a(n-1)+a(n-2)+8*(A010878(a(n-1))+A010878(a(n-2))))/9. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=Fib(n)-8*sum{1<k<n, Fib(n-k+1)*floor(a(k)/9)} where Fib(n)=A000045(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
|
|
CROSSREFS
|
Cf. A000045, A010073, A010074, A010075, A010077, A131294, A131295, A131296, A131297, A131318, A131319, A131320.
Adjacent sequences: A010073 A010074 A010075 this_sequence A010077 A010078 A010079
Sequence in context: A010077 A065076 A069638 this_sequence A138183 A076591 A078695
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
njas, Leonid Broukhis (leo(AT)mailcom.com)
|
|
|
Search completed in 0.002 seconds
|
