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A131320
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2*n - maximal value arising in the sequence S(n) representing the digital sum analogue base n of the Fibonacci recurrence.
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13
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1, 2, 3, 3, 5, 3, 3, 3, 5, 3, 3, 11, 7, 3, 3, 6, 9, 3, 3, 8, 9, 10, 11, 3, 9, 3, 3, 3, 15, 26, 8, 13, 10, 12, 3, 11, 19, 3, 23, 13, 13, 3, 21, 3, 23, 10, 3, 3, 9, 3, 3, 16, 17, 3, 3, 23, 17, 19, 29, 22, 11, 3, 17, 10, 25, 3, 22, 3, 35, 30, 11, 29, 57, 3, 3, 17, 65, 16, 13, 20, 21, 3, 3
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OFFSET
| 1,2
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COMMENTS
| The inequality a(n)>=3 holds for n>2.
a(n)=3 arises infinitely often; lim inf a(n)=3 for n-->oo.
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FORMULA
| a(n)=2n-A131319(n).
a(Lucas(2n))=3 where Lucas(n)=A000032(n).
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EXAMPLE
| a(3)=3, since the digital sum analogue base 3 of the Fibonacci sequence is 0,1,1,2,3,3,2,3,3,... where the pattern {2,3,3} is the periodic part (see A131294) and so has a maximal value of 3 which implies 2*3-3=3. a(9)=5, because the pattern here is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13 and so 2*9-13=5.
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CROSSREFS
| Cf. A000032, A000045, A000032, A131318, A131320.
See A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analogue of the Fibonacci sequence (in different bases).
Sequence in context: A205130 A069461 A063256 * A119912 A076368 A071049
Adjacent sequences: A131317 A131318 A131319 * A131321 A131322 A131323
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KEYWORD
| nonn
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AUTHOR
| Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jul 08 2007
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