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A260424 a(1) = 1, a(A206074(n)) = prime(a(n)), a(A205783(1+n)) = composite(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

%I A260424 #22 Jul 27 2015 22:12:42
%S A260424 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,29,25,
%T A260424 26,27,31,28,37,30,32,33,34,35,41,36,44,38,43,39,47,40,46,42,53,54,45,
%U A260424 48,49,50,59,51,61,58,52,63,67,55,71,62,56,66,57,65,73,60,79,75,83,76,89,64,68,69,109,70,97,82,101,72,103,85,81,74,127
%N A260424 a(1) = 1, a(A206074(n)) = prime(a(n)), a(A205783(1+n)) = composite(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.
%C A260424 After 1, each term of A206075 resides in a separate infinite cycle. This follows because primes (A000040) is a subsequence of A206074 [see _Thomas Ordowski_'s Feb 19 2014 comment in A206074] and thus each composite in A206074 is trapped into a trajectory containing only primes.
%H A260424 Antti Karttunen, <a href="/A260424/b260424.txt">Table of n, a(n) for n = 1..8192</a>
%H A260424 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A260424 a(1) = 1; for n > 1, if A257000(n) = 1 [when n is in A206074], then a(n) = A000040(a(A255574(n))), otherwise [when n is in A205783], a(n) = A002808(a(A255572(n))).
%F A260424 As a composition of related permutations:
%F A260424 a(n) = A246378(A260421(n)).
%F A260424 a(n) = A245704(A260426(n)).
%o A260424 (PARI)
%o A260424 allocatemem(123456789);
%o A260424 default(primelimit,4294965247);
%o A260424 uplim = 2^20;
%o A260424 v255574 = vector(uplim); A255574 = n -> v255574[n];
%o A260424 A255572 = n -> (n - A255574(n) - 1);
%o A260424 A257000(n) = polisirreducible(Pol(binary(n)));
%o A260424 v255574[1] = 0; i=0; j=0; n=2; while((n < uplim), v255574[n] = v255574[n-1]+A257000(n); n++);
%o A260424 A002808(n)={ my(k=-1); while( -n + n += -k + k=primepi(n), ); n}; \\ This function from _M. F. Hasler_
%o A260424 A260424(n) = if(1==n, 1, if(A257000(n), prime(A260424(A255574(n))), A002808(A260424(A255572(n)))));
%o A260424 for(n=1, 8192, write("b260424.txt", n, " ", A260424(n)));
%Y A260424 Inverse: A260423.
%Y A260424 Related permutations: A245704, A246378, A260421, A260426.
%Y A260424 Cf. A000040, A002808, A205783, A206074, A206075, A257000, A255572, A255574.
%K A260424 nonn
%O A260424 1,2
%A A260424 _Antti Karttunen_, Jul 25 2015