This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A138608 #11 May 17 2025 00:34:10
%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 n-th 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="https://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="/index/Per#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.
%K A138608 easy,nonn
%O A138608 1,2
%A A138608 _Ctibor O. Zizka_, May 14 2008
%E A138608 Edited, extended, starting offset changed from 0 to 1, and Scheme-code added by _Antti Karttunen_, Oct 05 2009