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 A131319 Maximal value arising in the sequence S(n) representing the digital sum analogue base n of the Fibonacci recurrence. 12
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS FORMULA For n=Lucas(2m)=A000032(2m) with m>0, we have a(n)=2n-3. a(n)=2n-A131320(n). EXAMPLE 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. CROSSREFS 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 KEYWORD nonn,base AUTHOR Hieronymus Fischer, Jul 08 2007 STATUS approved

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