Search: id:A010077
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%I A010077
%S A010077 0,1,1,2,3,5,8,13,12,7,10,8,9,17,17,16,15,13,10,5,6,11,8,10,9,10,10,
%T A010077 2,3,5,8,13,12,7,10,8,9,17,17,16,15,13,10,5,6,11,8,10,9,10,10,
%U A010077 2,3,5,8,13,12,7,10,8,9,17,17,16,15,13,10,5,6,11,8,10,9,10,10
%N A010077 a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) 
               = 1.
%C A010077 The digital sum analogue (in base 10) of the Fibonacci recurrence. - 
               Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%C A010077 a(n) and Fib(n)=A000045(n) are congruent modulo 9 which implies that 
               (a(n) mod 9) is equal to (Fib(n) mod 9) = A007887(n). Thus (a(n) 
               mod 9) is periodic with the Pisano period A001175(9)=24. - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%C A010077 a(n)==A004090(n) modulo 9 (A004090(n)=digital sum of Fib(n)). - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%C A010077 For general bases p>2, we have the inequality 2<=a(n)<=2p-3 (for n>2). 
               Actually, a(n)<=17=A131319(10) for the base p=10. - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%F A010077 Periodic from n=3 with period 24. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), 
               Mar 13 2006
%F A010077 a(n) = A030132(n-4) + A030132(n-3) for n>3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jul 04 2007
%F A010077 a(n)=a(n-1)+a(n-2)-9*(floor(a(n-1)/10)+floor(a(n-2)/10)). - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%F A010077 a(n)=floor(a(n-1)/10)+floor(a(n-2)/10)+(a(n-1)mod 10)+(a(n-2)mod 10). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%F A010077 a(n)=A059995(a(n-1))+A059995(a(n-2))+A010879(a(n-1))+A010879(a(n-2)). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%F A010077 a(n)=Fib(n)-9*sum{1<k<n, Fib(n-k+1)*floor(a(k)/10)} where Fib(n)=A000045(n). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
%t A010077 a[0] = 0; a[1] = 1; a[n_] := a[n] = Apply[ Plus, IntegerDigits[ a[n - 
               1] ]] + Apply[ Plus, IntegerDigits[ a[n - 2] ]]; Table[ a[n], {n, 
               0, 100} ]
%Y A010077 Cf. A007953, A007612, A065076.
%Y A010077 Cf. A000045, A010073, A010074, A010075, A010076, A131294, A131295, A131296, 
               A131297, A131318, A131319, A131320.
%Y A010077 Sequence in context: A104701 A074867 A131297 this_sequence A065076 A069638 
               A010076
%Y A010077 Adjacent sequences: A010074 A010075 A010076 this_sequence A010078 A010079 
               A010080
%K A010077 nonn,base
%O A010077 0,4
%A A010077 N. J. A. Sloane (njas(AT)research.att.com), Leonid Broukhis (leo(AT)mailcom.com)

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