cp's OEIS Frontend

A245702 Permutation of natural numbers: a(1) = 1, a(2n) = A014580(a(n)), a(2n+1) = A091242(a(n)), where A014580(n) = binary code for n-th irreducible polynomial over GF(2) and A091242(n) = binary code for n-th reducible polynomial over GF(2).

%I A245702 #19 Apr 01 2025 17:48:18
%S A245702 1,2,4,3,5,11,8,7,6,13,9,47,17,31,14,25,12,19,10,59,20,37,15,319,62,
%T A245702 87,24,185,42,61,21,137,34,55,18,97,27,41,16,415,76,103,28,229,49,67,
%U A245702 22,3053,373,433,79,647,108,131,33,1627,222,283,54,425,78,109,29,1123,166,203,45,379,71,91,26,731,121,145,36,253,53,73,23
%N A245702 Permutation of natural numbers: a(1) = 1, a(2n) = A014580(a(n)), a(2n+1) = A091242(a(n)), where A014580(n) = binary code for n-th irreducible polynomial over GF(2) and A091242(n) = binary code for n-th reducible polynomial over GF(2).
%H A245702 Antti Karttunen, <a href="/A245702/b245702.txt">Table of n, a(n) for n = 1..383</a>
%H A245702 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A245702 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A245702 a(1) = 1, a(2n) = A014580(a(n)), a(2n+1) = A091242(a(n)).
%F A245702 As a composition of related permutations:
%F A245702 a(n) = A245703(A227413(n)).
%F A245702 Other identities:
%F A245702 For all n >= 1, 1 - A091225(a(n)) = A000035(n). [Maps even numbers to binary representations of irreducible GF(2) polynomials (= A014580) and odd numbers to the corresponding representations of reducible polynomials].
%o A245702 (PARI)
%o A245702 allocatemem(123456789);
%o A245702 a014580 = vector(2^18);
%o A245702 a091242 = vector(2^22);
%o A245702 isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from _Charles R Greathouse IV_
%o A245702 i=0; j=0; n=2; while((n < 2^22), if(isA014580(n), i++; a014580[i] = n, j++; a091242[j] = n); n++)
%o A245702 A245702(n) = if(1==n, 1, if(0==(n%2), a014580[A245702(n/2)], a091242[A245702((n-1)/2)]));
%o A245702 for(n=1, 383, write("b245702.txt", n, " ", A245702(n)));
%o A245702 (Scheme)
%o A245702 ;; With memoizing definec-macro.
%o A245702 (definec (A245702 n) (cond ((< n 2) n) ((even? n) (A014580 (A245702 (/ n 2)))) (else (A091242 (A245702 (/ (- n 1) 2))))))
%Y A245702 Inverse: A245701.
%Y A245702 Cf. A000035, A014580, A091242, A091225.
%Y A245702 Similar entanglement permutations: A193231, A227413, A237126, A243288, A245703, A245704.
%K A245702 nonn
%O A245702 1,2
%A A245702 _Antti Karttunen_, Aug 02 2014