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Search: id:A010075
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| A010075 |
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a(n) = sum of base 8 digits of a(n-1) + sum of base 8 digits of a(n-2). |
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+0
13
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| 0, 1, 1, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8, 7, 8, 8, 2, 3, 5, 8, 6, 7, 13, 13, 12, 11, 9, 6, 8
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The digital sum analogue (in base 8) of the Fibonacci recurrence. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n) and Fib(n)=A000045(n) are congruent modulo 7 which implies that (a(n) mod 7) is equal to (Fib(n) mod 7). Thus (a(n) mod 7) is periodic with the Pisano period A001175(7)=16. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)==A004090(n) modulo 7 (A004090(n)=digital sum of Fib(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
For general bases p>2, the inequality 2<=a(n)<=2p-3 holds for n>2. Actually, a(n)<=11=A131319(8) for the base p=8. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
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FORMULA
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Periodic from n=3 with period 16. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 13 2006
a(n)=a(n-1)+a(n-2)-7*(floor(a(n-1)/8)+floor(a(n-2)/8)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=floor(a(n-1)/8)+floor(a(n-2)/8)+(a(n-1)mod 8)+(a(n-2)mod 8). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=(a(n-1)+a(n-2)+7*(A010877(a(n-1))+A010877(a(n-2))))/8. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=Fib(n)-7*sum{1<k<n, Fib(n-k+1)*floor(a(k)/8)} where Fib(n)=A000045(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
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CROSSREFS
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Cf. A000045, A010073, A010074, A010076, A010077, A131294, A131295, A131296, A131297, A131318, A131319, A131320.
Adjacent sequences: A010072 A010073 A010074 this_sequence A010076 A010077 A010078
Sequence in context: A011158 A104647 A065115 this_sequence A010074 A116918 A116917
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KEYWORD
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nonn,base
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AUTHOR
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njas, Leonid Broukhis (leo(AT)mailcom.com)
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