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A131319
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Maximal value arising in the sequence S(n) representing the digital sum analogue base n of the Fibonacci recurrence.
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12
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1, 2, 3, 5, 5, 9, 11, 13, 13, 17, 19, 13, 19, 25, 27, 26, 25, 33, 35, 32, 33, 34, 35, 45, 41, 49, 51, 53, 43, 34, 54, 51, 56, 56, 67, 61, 55, 73, 55, 67, 69, 81, 65, 85, 67, 82, 91, 93, 89, 97, 99, 88, 89, 105, 107, 89, 97, 97, 89, 98, 111, 121, 109, 118, 105, 129, 112
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OFFSET
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1,2
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COMMENTS
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The respective period lengths of S(n) are given by A001175(n-1) (which is the Pisano period to n-1) for n>=2.
The inequality a(n)<=2n-3 holds for n>2.
a(n)=2n-3 infinitely often; lim sup a(n)/n=2 for n-->oo.
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LINKS
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Table of n, a(n) for n=1..67.
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FORMULA
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For n=Lucas(2m)=A000032(2m) with m>0, we have a(n)=2n-3.
a(n)=2n-A131320(n).
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EXAMPLE
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a(3)=3, since the digital sum analogue base 3 of the Fibonacci sequence is S(3)=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.
a(9)=13 because the pattern base 9 is {2,3,5,8,13,13,10,7,9,8,9,9} (see A010076) where the maximal value is 13.
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CROSSREFS
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Cf. A000032, A000045, A131318, A131320.
See A010074, A010075, A010076, A010077, A131294, A131295, A131296, A131297 for the definition of the digital sum analogue of the Fibonacci recurrence(in different bases).
Sequence in context: A096736 A128188 A139127 * A108962 A091608 A183562
Adjacent sequences: A131316 A131317 A131318 * A131320 A131321 A131322
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KEYWORD
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nonn,base
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AUTHOR
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Hieronymus Fischer, Jul 08 2007
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STATUS
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approved
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