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A246205 Permutation of natural numbers: a(1) = 1, a(A014580(n)) = A117968(a(n)), a(A091242(n)) = A117967(1+a(n)), where A117967 and A117968 give positive and negative parts of inverse of balanced ternary enumeration of integers, and A014580 resp. A091242 are the binary coded irreducible resp. reducible polynomials over GF(2). 3

%I #10 Aug 21 2014 00:00:31

%S 1,2,7,5,3,11,23,15,4,12,22,33,6,52,17,13,35,43,25,16,137,45,53,36,58,

%T 155,29,47,462,154,66,135,37,152,426,30,8,156,1273,428,24,148,460,41,

%U 423,1426,71,31,9,427,4283,1410,34,431,75,1274,159,1423,21,3707,194,99,44,10,1412,11115,64,3850,38,1404,103,4281,26,412,3722,49

%N Permutation of natural numbers: a(1) = 1, a(A014580(n)) = A117968(a(n)), a(A091242(n)) = A117967(1+a(n)), where A117967 and A117968 give positive and negative parts of inverse of balanced ternary enumeration of integers, and A014580 resp. A091242 are the binary coded irreducible resp. reducible polynomials over GF(2).

%H Antti Karttunen, <a href="/A246205/b246205.txt">Table of n, a(n) for n = 1..10001</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(1) = 1, and for n > 1, if A091225(n) = 1 [i.e. n is in A014580], a(n) = A117968(a(A091226(n))), otherwise a(n) = A117967(1+a(A091245(n))).

%F As a composition of related permutations:

%F a(n) = A246207(A245701(n)).

%F a(n) = A246209(A246201(n)).

%o (Scheme, with memoization-macro definec)

%o (definec (A246205 n) (cond ((= 1 n) n) ((= 1 (A091225 n)) (A117968 (A246205 (A091226 n)))) (else (A117967 (+ 1 (A246205 (A091245 n)))))))

%Y Inverse: A246206.

%Y Similar or related entanglement permutations: A246163, A245701, A246201, A246207, A246209.

%Y Cf. A014580, A091225, A091226, A091242, A091245, A117967, A117968.

%K nonn

%O 1,2

%A _Antti Karttunen_, Aug 19 2014

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