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A260423 a(1) = 1, a(prime(n)) = A206074(a(n)), a(composite(n)) = A205783(1+a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

%I A260423 #21 Jul 28 2015 12:40:08
%S A260423 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,26,27,
%T A260423 28,30,25,32,29,33,34,35,36,38,31,40,42,44,37,46,41,39,49,45,43,50,51,
%U A260423 52,54,57,47,48,60,63,65,56,53,68,55,62,58,74,66,64,59,75,76,78,61,82,67,86,70,72,92,95,69,98,85,80,71,102,84,94,88,111
%N A260423 a(1) = 1, a(prime(n)) = A206074(a(n)), a(composite(n)) = A205783(1+a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.
%H A260423 Antti Karttunen, <a href="/A260423/b260423.txt">Table of n, a(n) for n = 1..10001</a>
%H A260423 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A260423 a(1) = 1; for n > 1, if A010051(n) = 1 [when n is a prime], then a(n) = A206074(a(A000720(n))), otherwise [when n is a composite], a(n) = A205783(1+a(A065855(n))).
%F A260423 As a composition of related permutations:
%F A260423 a(n) = A260422(A246377(n)).
%F A260423 a(n) = A260425(A245703(n)).
%o A260423 (PARI)
%o A260423 allocatemem(123456789);
%o A260423 default(primelimit,4294965247);
%o A260423 uplim = 2^23;
%o A260423 v206074 = vector(uplim); A206074 = n -> v206074[n];
%o A260423 v205783 = vector(uplim); A205783 = n -> v205783[n];
%o A260423 isA206074(n) = polisirreducible(Pol(binary(n)));
%o A260423 v205783[1] = 1; i=0; j=1; n=2; while((n < uplim), if(!(n%65536),print1(n,", ")); if(isA206074(n), i++; v206074[i] = n, j++; v205783[j] = n); n++); print(n);
%o A260423 A260423(n) = if(1==n, 1, if(isprime(n), A206074(A260423(primepi(n))), A205783(1+A260423(n-primepi(n)-1))));
%o A260423 for(n=1, 10001, write("b260423.txt", n, " ", A260423(n)));
%o A260423 (Scheme) (definec (A260423 n) (cond ((<= n 1) n) ((= 1 (A010051 n)) (A206074 (A260423 (A000720 n)))) (else (A205783 (+ 1 (A260423 (A065855 n)))))))
%Y A260423 Inverse: A260424.
%Y A260423 Related permutations: A245703, A246377, A260422, A260425.
%Y A260423 Cf. A000040, A002808, A010051, A000720, A065855, A205783, A206074.
%K A260423 nonn,look
%O A260423 1,2
%A A260423 _Antti Karttunen_, Jul 25 2015