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A074867
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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.
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2
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Periodic with least period 60. - Christopher N. Swanson (cswanson(AT)ashland.edu), Jul 22 2003
The digital product analogue (in base 10) of the Fibonacci recurrence. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
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
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
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
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FORMULA
| 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
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
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
a(n)=A131297(n) if A131297(n)<=10. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 01 2007
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
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
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CROSSREFS
| Cf. A000045.
Cf. A000045, A010073, A010074, A010075, A010076, A131294, A131295, A131296, A131297, A131318, A131319, A131320.
Sequence in context: A106005 A105995 A104701 * A131297 A010077 A065076
Adjacent sequences: A074864 A074865 A074866 * A074868 A074869 A074870
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KEYWORD
| base,easy,nonn
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AUTHOR
| Felice Russo (frusso(AT)micron.com), Sep 11 2002
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EXTENSIONS
| More terms from Christopher N. Swanson (cswanson(AT)ashland.edu), Jul 22 2003
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