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%I A010077 #30 May 27 2021 06:25:42
%S A010077 0,1,1,2,3,5,8,13,12,7,10,8,9,17,17,16,15,13,10,5,6,11,8,10,9,10,10,2,
%T A010077 3,5,8,13,12,7,10,8,9,17,17,16,15,13,10,5,6,11,8,10,9,10,10,2,3,5,8,
%U A010077 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 analog (in base 10) of the Fibonacci recurrence. - _Hieronymus Fischer_, Jun 27 2007
%C A010077 a(n) and Fibonacci(n) = A000045(n) are congruent modulo 9 which implies that (a(n) mod 9) is equal to (Fibonacci(n) mod 9) = A007887(n). Thus (a(n) mod 9) is periodic with the Pisano period A001175(9)=24. - _Hieronymus Fischer_, Jun 27 2007
%C A010077 a(n) == A004090(n) (mod 9) (A004090(n) = digital sum of Fibonacci(n)). - _Hieronymus Fischer_, 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_, Jun 27 2007
%H A010077 David A. Corneth, <a href="/A010077/b010077.txt">Table of n, a(n) for n = 0..9999</a>
%H A010077 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%F A010077 Periodic from n=3 with period 24. - _Franklin T. Adams-Watters_, Mar 13 2006
%F A010077 a(n) = A030132(n-4) + A030132(n-3) for n>3. - _Reinhard Zumkeller_, 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_, 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_, 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_, Jun 27 2007
%F A010077 a(n) = Fibonacci(n) - 9*Sum_{k=2..n-1} Fibonacci(n-k+1)*floor(a(k)/10) where Fibonacci(n) = A000045(n). - _Hieronymus Fischer_, 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} ]
%t A010077 nxt[{a_,b_}]:={b, Total[IntegerDigits[a]]+Total[IntegerDigits[b]]}; NestList[ nxt,{0,1},80][[All,1]] (* _Harvey P. Dale_, Apr 15 2018 *)
%o A010077 (PARI) first(n) = {n = max(n, 2); my(res = vector(n)); res[2] = 1; for(i = 3, n, res[i] = sumdigits(res[i-1]) + sumdigits(res[i-2]) ); res } \\ _David A. Corneth_, May 26 2021
%Y A010077 Cf. A007953, A007612, A065076.
%Y A010077 Cf. A000045, A010073, A010074, A010075, A010076.
%Y A010077 Cf. A131294, A131295, A131296, A131297, A131318, A131319, A131320.
%K A010077 nonn,easy,base
%O A010077 0,4
%A A010077 _N. J. A. Sloane_, _Leonid Broukhis_

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