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A074867 a(n) = M(a(n-1)) + M(a(n-2)) where a(1)=a(2)=1 and M(k) is the product of the digits of k in base 10. 3
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; text; internal format)
OFFSET
1,3
COMMENTS
Periodic with least period 60. - Christopher N. Swanson (cswanson(AT)ashland.edu), Jul 22 2003
From Hieronymus Fischer, Jul 01 2007: (Start)
The digital product analog (in base 10) of the Fibonacci recurrence.
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.
a(n)==A131297(n) modulo 10 (A131297(n)=digital sum analog base 11 of the Fibonacci recurrence).
For general bases p>1, we have the inequality 1<=a(n)<=2p-2 (for n>0). Actually, a(n)<=18.
(End)
LINKS
FORMULA
From Hieronymus Fischer, Jul 01 2007: (Start)
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.
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.
a(n) = (a(n-1)mod 10)+(a(n-2)mod 10) = A010879(a(n-1))+A010879(a(n-2)).
a(n) = A131297(n) if A131297(n)<=10.
a(n) = Fib(n)-10*sum{1<k<n, Fib(n-k+1)*floor(a(k)/10)} where Fib(n)=A000045(n).
a(n) = A000045(n)-10*sum{1<k<n, A000045(n-k+1)*A059995(a(k))}. (End)
MATHEMATICA
nxt[{a_, b_}]:={b, Times@@IntegerDigits[a]+Times@@IntegerDigits[b]}; Transpose[ NestList[nxt, {1, 1}, 90]][[1]] (* Harvey P. Dale, Feb 01 2015 *)
CROSSREFS
Sequence in context: A104701 A309782 A300999 * A131297 A267809 A010077
KEYWORD
base,easy,nonn
AUTHOR
Felice Russo, Sep 11 2002
EXTENSIONS
More terms from Christopher N. Swanson (cswanson(AT)ashland.edu), Jul 22 2003
Definition adapted to offset by Georg Fischer, Jun 18 2021
STATUS
approved

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)