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A138607 List first A008578(1) odd numbers, then first A008578(2) even numbers, then the next A008578(3) odd numbers, then the next A008578(4) even numbers, etc.

%I A138607 #19 Mar 15 2022 08:16:42
%S A138607 1,2,4,3,5,7,6,8,10,12,14,9,11,13,15,17,19,21,16,18,20,22,24,26,28,30,
%T A138607 32,34,36,23,25,27,29,31,33,35,37,39,41,43,45,47,38,40,42,44,46,48,50,
%U A138607 52,54,56,58,60,62,64,66,68,70,49,51,53,55,57,59,61,63,65,67,69,71,73
%N A138607 List first A008578(1) odd numbers, then first A008578(2) even numbers, then the next A008578(3) odd numbers, then the next A008578(4) even numbers, etc.
%C A138607 A permutation of numbers.
%H A138607 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A138607 If n < 3, a(n) = n. If n-2 = A007504(A083375(n-2)), then a(n) = a(n-1-A000040(A083375(n-2)))+2, otherwise a(n) = a(n-1)+2. - _Antti Karttunen_, Oct 05 2009.
%e A138607 Let
%e A138607   S1={1}
%e A138607   S2={2,4}
%e A138607   S3={3,5,7}
%e A138607   S4={6,8,10,12,14}
%e A138607   S5={9,11,13,15,17,19,21}
%e A138607   S6={16,18,20,22,24,26,28,30,32,34,36}
%e A138607   ...
%e A138607 then S1, S2, S3, S4, S5, S6,... gives this sequence.
%o A138607 (MIT Scheme:) (define (A138607 n) (if (< n 3) n (let ((k (A083375 (- n 2)))) (if (= (- n 2) (A007504 k)) (+ 2 (A138607 (- n 1 (A000040 k)))) (+ 2 (A138607 (-1+ n))))))) ;; _Antti Karttunen_, Oct 05 2009
%Y A138607 Inverse: A166014. Cf. A138606, A138608, A138609, A138612.
%K A138607 nonn,tabf
%O A138607 1,2
%A A138607 _Ctibor O. Zizka_, May 14 2008
%E A138607 Edited, extended, and offset changed from 0 to 1 by _Antti Karttunen_, Oct 05 2009