Search: id:A074867
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%I A074867
%S A074867 1,1,2,3,5,8,13,11,4,5,9,14,13,7,10,7,7,14,11,5,6,11,7,8,15,13,8,11,9,
%T A074867 10,9,9,18,17,15,12,7,9,16,15,11,6,7,13,10,3,3,6,9,15,14,9,13,12,5,7,12,
%U A074867 9,11,10,1,1,2,3,5,8,13,11,4,5,9,14,13,7,10,7,7,14,11,5,6,11,7,8,15,13
%N A074867 a(n)=M[a(n-1)]+M[a(n-2)] where a(0)=a(1)=1 and M(n) is the product of 
               the digits of n in base 10.
%C A074867 Periodic with least period 60. - Christopher N. Swanson (cswanson(AT)ashland.edu), 
               Jul 22 2003
%C A074867 The digital product analogue (in base 10) of the Fibonacci recurrence. 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
%C A074867 a(n) and Fib(n)=A000045(n) are congruent modulo 10 which implies that 
               (a(n) mod 10) is equal to (Fib(n) mod 10) = A003893(n). Thus (a(n) 
               mod 10) is periodic with the Pisano period A001175(10)=60. - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
%C A074867 a(n)==A131297(n) modulo 10 (A131297(n)=digital sum analogue base 11 of 
               the Fibonacci recurrence). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 01 2007
%C A074867 For general bases p>1, we have the inequality 1<=a(n)<=2p-2 (for n>0). 
               Actually, a(n)<=18. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 01 2007
%F A074867 a(n)=a(n-1)+a(n-2)-10*(floor(a(n-1)/10)+floor(a(n-2)/10)). This is valid, 
               since a(n)<100. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 01 2007
%F A074867 a(n)=ds_10(a(n-1))+ds_10(a(n-2))-(floor(a(n-1)/10)+floor(a(n-2)/10)) 
               where ds_10(x) is the digital sum of x in base 10. - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
%F A074867 a(n)=(a(n-1)mod 10)+(a(n-2)mod 10)=A010879(a(n-1))+A010879(a(n-2)). - 
               Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
%F A074867 a(n)=A131297(n) if A131297(n)<=10. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Jul 01 2007
%F A074867 a(n)=Fib(n)-10*sum{1<k<n, Fib(n-k+1)*floor(a(k)/10)} where Fib(n)=A000045(n). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
%F A074867 a(n)=A000045(n)-10*sum{1<k<n, A000045(n-k+1)*A059995(a(k))}. - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
%Y A074867 Cf. A000045.
%Y A074867 Cf. A000045, A010073, A010074, A010075, A010076, A131294, A131295, A131296, 
               A131297, A131318, A131319, A131320.
%Y A074867 Sequence in context: A106005 A105995 A104701 this_sequence A131297 A010077 
               A065076
%Y A074867 Adjacent sequences: A074864 A074865 A074866 this_sequence A074868 A074869 
               A074870
%K A074867 base,easy,nonn
%O A074867 1,3
%A A074867 Felice Russo (felice.russo(AT)katamail.com), Sep 11 2002
%E A074867 More terms from Christopher N. Swanson (cswanson(AT)ashland.edu), Jul 
               22 2003

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