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%I #12 Dec 10 2019 12:10:16
%S 1,3,2,7,6,5,4,16,13,12,10,15,9,27,11,8,22,21,18,25,46,17,43,35,20,14,
%T 36,32,34,29,26,42,40,69,28,65,54,23,33,24,55,85,50,52,45,31,41,62,19,
%U 60,100,44,67,95,80,64,37,51,38,53,82,122,78,158,75,77,68,48,61,91,49,30,88,143,145,66,98,136,116,115,93,63,56,76,58,79,39
%N Permutation of natural numbers: a(1) = 1, a(A233271(1+n)) = A179016(1+a(n)), a(A269390(n)) = A213713(a(n)), where A179016, A233271 are the infinite trunks of binary beanstalk and inverted binary beanstalk and A213713, A269390 their complements.
%H Antti Karttunen, <a href="/A269397/b269397.txt">Table of n, a(n) for n = 1..8191</a>
%H Antti Karttunen, <a href="/A135141/a135141.pdf">Entanglement Permutations</a>, 2016-2017
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, for n > 1, if A269381(n) - A269381(n-1) > 0 [when n is in A233271] a(n) = A179016(1+a(A269381(n)-1)), otherwise a(n) = A213713(a(n-A269381(n))).
%F As a composition of related permutations:
%F a(n) = A269402(A269391(n)).
%o (Scheme, with memoization-macro definec)
%o (definec (A269397 n) (cond ((<= n 1) n) ((zero? (- (A269381 n) (A269381 (- n 1)))) (A213713 (A269397 (- n (A269381 n))))) (else (A179016 (+ 1 (A269397 (+ -1 (A269381 n))))))))
%Y Inverse: A269398.
%Y Cf. A179016, A213713, A233271, A269381, A269390.
%Y Related or similar permutations: A269391, A269401, A269402.
%Y Cf. also A233270.
%K nonn,base,look
%O 1,2
%A _Antti Karttunen_, Mar 05 2016