cp's OEIS Frontend

A245813 Permutation of natural numbers induced when A091205 is restricted to {1} and binary codes for polynomials reducible over GF(2): a(1) = 1, a(n) = A062298(A091205(A091242(n-1))).

%I A245813 #7 Aug 18 2014 00:52:06
%S A245813 1,2,5,3,4,9,11,7,6,18,10,59,20,25,16,8,50,15,32,31,12,13,38,21,41,
%T A245813 125,85,43,17,45,52,35,22,19,103,105,33,24,14,190,68,27,66,28,161,29,
%U A245813 80,26,54,46,177,84,258,34,180,64,90,70,507,37,196,96,39,110,430,92,78,75,600,48,40,82,213,218,71,23,87,72,51,132,30
%N A245813 Permutation of natural numbers induced when A091205 is restricted to {1} and binary codes for polynomials reducible over GF(2): a(1) = 1, a(n) = A062298(A091205(A091242(n-1))).
%H A245813 Antti Karttunen, <a href="/A245813/b245813.txt">Table of n, a(n) for n = 1..10001</a>
%H A245813 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A245813 a(1) = 1, and for n > 1, a(n) = A062298(A091205(A091242(n-1))).
%F A245813 As a composition of related permutations:
%F A245813 a(n) = A245815(A245820(n)).
%o A245813 (PARI)
%o A245813 allocatemem(234567890);
%o A245813 v091226 = vector(2^22);
%o A245813 v091242 = vector(2^22);
%o A245813 isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from _Charles R Greathouse IV_
%o A245813 i=0; j=0; n=2; while((n < 2^22), if(isA014580(n), i++; v091226[n] = v091226[n-1]+1, j++; v091242[j] = n; v091226[n] = v091226[n-1]); n++);
%o A245813 A062298(n) = n-primepi(n);
%o A245813 A091226(n) = v091226[n];
%o A245813 A091242(n) = v091242[n];
%o A245813 A091205(n) = if(n<=1, n, if(isA014580(n), prime(A091205(A091226(n))), {my(irfs, t); irfs=subst(lift(factor(Mod(1, 2)*Pol(binary(n)))), x, 2); irfs[,1]=apply(t->A091205(t), irfs[,1]); factorback(irfs)}));
%o A245813 A245813(n) = if(n<=1, n, A062298(A091205(A091242(n-1))));
%o A245813 for(n=1, 10001, write("b245813.txt", n, " ", A245813(n)));
%o A245813 (Scheme) (define (A245813 n) (if (<= n 1) n (A062298 (A091205 (A091242 (- n 1))))))
%Y A245813 Inverse: A245814.
%Y A245813 Cf. A062298, A091242.
%Y A245813 Related permutations: A091205, A245815, A245820.
%K A245813 nonn
%O A245813 1,2
%A A245813 _Antti Karttunen_, Aug 16 2014