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A182601 Position (index) of the smallest Fibonacci number in a sequence of at least n consecutive composite Fibonacci numbers.

%I A182601 #9 Dec 24 2024 22:12:43
%S A182601 6,8,8,18,18,30,30,30,30,30,30,30,30,48,48,48,48,48,48,48,48,48,48,48,
%T A182601 48,48,48,48,48,48,48,48,48,48,48,84,84,84,84,84,84,84,84,84,84,84,84,
%U A182601 138,138,138
%N A182601 Position (index) of the smallest Fibonacci number in a sequence of at least n consecutive composite Fibonacci numbers.
%C A182601 All entries are of the form A001605(.)+1.
%C A182601 The records in A182600 are 1, 3, 5, 13, 35, 47, 221,... with first differences 2, 2, 8, 22, 12, 174,... and these are the frequencies (repetitions) of the entries in this sequence here.
%H A182601 Robert Israel, <a href="/A182601/b182601.txt">Table of n, a(n) for n = 1..10000</a>
%F A182601 min{ i: A000045(j) in A002808 for all j=i..i+n-1}.
%p A182601 # using b-file for A001605 as a list B001605
%p A182601 dB:= B001605[2..-1]-B001605[1..-2]:
%p A182601 f:= proc(n) local i;
%p A182601  for i from 1 do if dB[i] >= n+1 then return B001605[i]+1 fi od
%p A182601 end proc:
%p A182601 map(f, [$1..100]); # _Robert Israel_, Dec 24 2024
%Y A182601 Cf. A005478, A090206.
%K A182601 nonn
%O A182601 1,1
%A A182601 _R. J. Mathar_, Nov 22 2010