This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A010076 #30 Aug 25 2024 18:45:54
%S A010076 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,
%T A010076 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,
%U A010076 9,9,2,3,5,8,13,13,10,7,9,8,9,9
%N A010076 a(n) = sum of base-9 digits of a(n-1) + sum of base-9 digits of a(n-2).
%C A010076 The digital sum analog (in base 9) of the Fibonacci recurrence. - _Hieronymus Fischer_, Jun 27 2007
%C A010076 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_, Jun 27 2007
%C A010076 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_, Jun 27 2007
%H A010076 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%H A010076 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1).
%F A010076 Periodic from n=3 with period 12. - _Franklin T. Adams-Watters_, Mar 13 2006
%F A010076 From _Hieronymus Fischer_, Jun 27 2007: (Start)
%F A010076 a(n) = a(n-1)+a(n-2)-8*(floor(a(n-1)/9)+floor(a(n-2)/9)).
%F A010076 a(n) = floor(a(n-1)/9)+floor(a(n-2)/9)+(a(n-1)mod 9)+(a(n-2)mod 9).
%F A010076 a(n) = (a(n-1)+a(n-2)+8*(A010878(a(n-1))+A010878(a(n-2))))/9.
%F A010076 a(n) = Fib(n)-8*sum{1<k<n, Fib(n-k+1)*floor(a(k)/9)} where Fib(n)=A000045(n). (End)
%t A010076 PadRight[{0, 1, 1}, 100, {8, 9, 9, 2, 3, 5, 8, 13, 13, 10, 7, 9}] (* _Paolo Xausa_, Aug 25 2024 *)
%Y A010076 Cf. A000045, A001175, A010073, A010074, A010075, A010077, A010878, A079344, A131294, A131295, A131296, A131297, A131318, A131319, A131320.
%K A010076 nonn,base
%O A010076 0,4
%A A010076 _N. J. A. Sloane_, _Leonid Broukhis_
%E A010076 Incorrect comment removed by _Michel Marcus_, Apr 29 2018