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 A130633 #16 Feb 12 2025 09:26:43
%S A130633 0,0,0,0,0,0,0,1,1,1,2,2,1,1,2,1,2,2,3,2,2,2,2,3,2,3,3,3,2,2,2,2,2,2,
%T A130633 3,2,2,2,2,2,2,2,3,2,2,3,2,3,2,3,3,3,3,2,2,3,3,2,3,2,2,2,2,2,2,3,3,3,
%U A130633 2,3,2,3,2,3,3,3,3,3,2,3,3,3,3,3,2,3,2
%N A130633 Additive persistence of Fibonacci numbers.
%C A130633 Up to 10000 the maximum value is 4.
%C A130633 Up to 10^22 the maximum value is 4. Conjecture: for n > 15, a(n) > 1. I checked the conjecture up to 10^10. - _Charles R Greathouse IV_, Feb 12 2025
%F A130633 a(n) = A031286(A000045(n)). - _Michel Marcus_, Feb 12 2025
%e A130633 3524578 -> 3+5+2+4+5+7+8 = 34 -> 3+4 = 7 -> persistence = 2.
%p A130633 with(numtheory): with(combinat): P:=proc(n) local a,t; t:=0; a:=fibonacci(n); while a>9 do t:=t+1; a:=convert(convert(a,base,10),`+`); od; t;
%p A130633 end: seq(P(i),i=0..10^2);
%t A130633 Table[Length[NestWhileList[Plus@@IntegerDigits[#]&, Fibonacci[n], #>=10&]], {n, 0, 86}]-1 (* _James C. McMahon_, Feb 11 2025 *)
%o A130633 (PARI) ap(n)=my(s); while(n>9, n=sumdigits(n); s++); s
%o A130633 a(n)=ap(fibonacci(n)) \\ _Charles R Greathouse IV_, Feb 12 2025
%Y A130633 Cf. A000045, A031286.
%K A130633 easy,nonn,base
%O A130633 0,11
%A A130633 _Paolo P. Lava_ and _Giorgio Balzarotti_, Jun 19 2007, corrected Jun 22 2007
%E A130633 Corrected entries and changed Maple code by _Paolo P. Lava_, Dec 19 2017