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Search: id:A010077
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| A010077 |
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a(n) = sum of digits of a(n-1) + sum of digits of a(n-2); a(0) = 0, a(1) = 1. |
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+0
15
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| 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, 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, 13, 12, 7, 10, 8, 9, 17, 17, 16, 15, 13, 10, 5, 6, 11, 8, 10, 9, 10, 10
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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The digital sum analogue (in base 10) of the Fibonacci recurrence. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n) and Fib(n)=A000045(n) are congruent modulo 9 which implies that (a(n) mod 9) is equal to (Fib(n) mod 9) = A007887(n). Thus (a(n) mod 9) is periodic with the Pisano period A001175(9)=24. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)==A004090(n) modulo 9 (A004090(n)=digital sum of Fib(n)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
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 (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
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FORMULA
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Periodic from n=3 with period 24. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 13 2006
a(n) = A030132(n-4) + A030132(n-3) for n>3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 04 2007
a(n)=a(n-1)+a(n-2)-9*(floor(a(n-1)/10)+floor(a(n-2)/10)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=floor(a(n-1)/10)+floor(a(n-2)/10)+(a(n-1)mod 10)+(a(n-2)mod 10). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=A059995(a(n-1))+A059995(a(n-2))+A010879(a(n-1))+A010879(a(n-2)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
a(n)=Fib(n)-9*sum{1<k<n, Fib(n-k+1)*floor(a(k)/10)} where Fib(n)=A000045(n). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007
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MATHEMATICA
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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} ]
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CROSSREFS
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Cf. A007953, A007612, A065076.
Cf. A000045, A010073, A010074, A010075, A010076, A131294, A131295, A131296, A131297, A131318, A131319, A131320.
Sequence in context: A104701 A074867 A131297 this_sequence A065076 A069638 A010076
Adjacent sequences: A010074 A010075 A010076 this_sequence A010078 A010079 A010080
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Leonid Broukhis (leo(AT)mailcom.com)
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