%I A138608
%S A138608 1,2,3,6,4,7,10,5,8,11,14,17,9,12,15,18,21,24,27,30,13,16,19,22,25,28,
%T A138608 31,34,37,40,43,46,49,20,23,26,29,32,35,38,41,44,47,50,53,56,59,62,65,
%U A138608 68,71,74,77,80,33,36,39,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84
%N A138608 List first F(1) numbers from A016777, then first F(2) numbers from A016789, 
               then the first F(3) numbers from A008585 (starting from 3), then 
               the next F(4) numbers from A016777, then the next F(5) numbers from 
               A016789, then the next F(6) numbers from A008585, etc, where F(n) 
               = A000045(n), the nth Fibonacci number.
%C A138608 The original name was "Generalized FibCon sequence". However, this sequence 
               has only a passing resemblance to Connell-like sequences (see A001614 
               and the paper by Iannucci & Mills-Taylor), which are all monotone, 
               while this sequence is a bijection of natural numbers.
%H A138608 Douglas E. Iannucci, Donna Mills-Taylor, <A HREF="http://www.cs.uwaterloo.ca/
               journals/JIS/IANN/iann1.html">On Generalizing the Connell Sequence</
               A>, Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.7
%H A138608 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A138608 If n < 4, a(n) = n. If n = A000045(A072649(n)+1), then a(n) = a(n-1-A000045(A072649(n)))+3, 
               otherwise a(n) = a(n-1)+3. - Antti Karttunen, Oct 05 2009.
%F A138608 1. The sequence is formed by concatenating subsequences S0,S1, S2, ..., 
               each of finite length. 2. The subsequence S0 consists of the element 
               1. 3. The n-th subsequence has F(n) elements, F(n) denotes n-th Fibonacci 
               number. 4. Each subsequence is nondecreasing and the difference between 
               two consecutive elements in the same subsequence is 3.
%e A138608 Let us separate natural numbers into three disjoint sets (A016777, A016789 
               and A008585):
%e A138608 1,4,7,10,13,16,19,22,25,28,31,...
%e A138608 2,5,8,11,14,17,20,23,26,29,32,...
%e A138608 3,6,9,12,15,18,21,24,27,30,33,...
%e A138608 then
%e A138608 S0={1}
%e A138608 S1={2}
%e A138608 S2={3,6}
%e A138608 S3={4,7,10}
%e A138608 S4={5,8,11,14,17}
%e A138608 S5={9,12,15,18,21,24,27,30}
%e A138608 ...
%e A138608 and concatenating S0/S1/S2/S3/S4/S5/... gives this sequence.
%o A138608 (MIT Scheme:) (define (A138608 n) (if (< n 4) n (let ((k (A072649 n))) 
               (if (= n (A000045 (1+ k))) (+ 3 (A138608 (- n 1 (A000045 k)))) (+ 
               3 (A138608 (-1+ n)))))))
%Y A138608 Inverse: A166015. A010872(a(n)) = A010872(A072649(n)). Cf. A138606-A138609, 
               A138612.
%Y A138608 Sequence in context: A156688 A019567 A098286 this_sequence A092283 A099900 
               A138728
%Y A138608 Adjacent sequences: A138605 A138606 A138607 this_sequence A138609 A138610 
               A138611
%K A138608 easy,nonn
%O A138608 1,2
%A A138608 Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), May 14 2008
%E A138608 Edited, extended, starting offset changed from 0 to 1, and Scheme-code 
               added by Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), 
               Oct 05 2009