

A202805


a(n) is the largest p in an n_nacci(p) sequence (Fibonacci(p) for n=2, tribonacci(p) for n=3, etc.) such that n_nacci(p) >= 2^(pn1).


0



6, 12, 25, 48, 94, 184, 363, 719, 1430, 2851, 5691, 11371, 22728, 45443, 90870
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OFFSET

2,1


COMMENTS

All n_nacci sequences whose first n1 terms are zeros followed by 1 are complete sequences. As n increases, the terms n+1,...,2n are 1,2,..,2^n (ascending powers of 2). In the limit as n tends to infinity the n_nacci sequence after an initial infinite set of zeros followed by 1 has successive terms of increasing powers of 2. This limiting sequence is the most minimal complete sequence. Consequently for each n_nacci(p) sequence there must be a largest p where n_nacci(p) >= 2^(pn1).


LINKS

Table of n, a(n) for n=2..16.
Wikipedia, Complete sequence.


FORMULA

a(n)=(greatest term of n_nacci(p)) >= 2^(pn1).


EXAMPLE

For n=3, the tribonnaci sequence is 0,0,1,1,2,4,7,...,149,274,504,... and the 13th term is 504 < 512 so a(n)=12 because 274 is greatest term >= 2^(1231) = 256.


MATHEMATICA

fib[n_, m_] := (Block[{nacci}, (Do[nacci[g]=0, {g, 0, m  2}]; nacci[m1]=1; nacci[p_] := (nacci[p]=Sum[nacci[h], {h, pm, p1}]); nacci[n])]); crossover[q_] := (Block[{$RecursionLimit=Infinity}, (k=0; While[fib[k+q+1, q]>=2^k, k++]; k+q)]); Table[crossover[j], {j, 2, 12}]


CROSSREFS

Cf. A000045, A000073, A000078.
Sequence in context: A110959 A303398 A244743 * A065106 A264008 A283221
Adjacent sequences: A202802 A202803 A202804 * A202806 A202807 A202808


KEYWORD

nonn


AUTHOR

Frank M Jackson, Dec 24 2011


STATUS

approved



