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A260719 a(n) = A091222(A260735(n)): number of irreducible factors (in ring GF(2)[X]) of the binary encoded polynomial obtained after the n-th iteration of A234742, when starting with the initial value 455.

%I A260719 #19 Aug 06 2015 07:43:51
%S A260719 5,5,3,4,3,5,9,2,7,2,6,6,2,2,2,3,8,8,6,5,5,7,6,4,5,6,2,7,6,4,5,4,5,4,
%T A260719 5,9,4,10,3,4,7,4,4,3,4,3,5,8,6,4,7,5,3,7,3,3,3,3,3,7,3,5,6,6,9,4,9,3,
%U A260719 5,6,3,4,5,7,7,4,5,2,10,11,6,6,7,13,4,6,5,10,6,4,7,4,10,8,3,7,7,4,5,5,2,4,8,3,4,3,7,4,6,3,15,3,4,7,6,6,6,5,5,8,4
%N A260719 a(n) = A091222(A260735(n)): number of irreducible factors (in ring GF(2)[X]) of the binary encoded polynomial obtained after the n-th iteration of A234742, when starting with the initial value 455.
%C A260719 Records occur in positions 0, 6, 37, 79, 83, 110, 329, 554, 1019, 1318, 2027, and they are 5, 9, 10, 11, 13, 15, 16, 17, 20, 21, 23.
%C A260719 First 2's occur at positions 7, 9, 12, 13, 14, 26, 77, 100, 127, 158, 161, 173, 183, 193, 201, 208, 442, 447, 528, 544, 642, 706, 1033, 1089, 1222, 1831.
%C A260719 Note that if this sequence ever obtains value 1, then the rest of terms are also 1's, as then A260735 has attained as its constant value one of the terms of A091214 (which is a subsequence of A235035, the fixed points of A234742).
%H A260719 Antti Karttunen, <a href="/A260719/b260719.txt">Table of n, a(n) for n = 0..2049</a>
%F A260719 a(n) = A091222(A260735(n)).
%e A260719 See example in A260735. This sequence gives the number of those irreducible factors (in ring GF(2)[X], not necessarily all primes in Z) that are multiplied together (in ordinary way) to get the next term of A260735. For example, a(0) = 5 (for 3 * 3 * 7 * 7 * 7), a(1) = 5 (for 3 * 7 * 7 * 13 * 13).
%o A260719 (PARI)
%o A260719 allocatemem((2^30));
%o A260719 {my(n=455, fm); for(i=0,2049, fm=factor(Pol(binary(n))*Mod(1, 2)); write("b260719.txt", i, " ", sum(k=1, #fm~, fm[k, 2])); n = factorback(subst(lift(fm),x,2))); };
%o A260719 (Scheme) (define (A260719 n) (A091222 (A260735 n)))
%Y A260719 Cf. A091214, A091222, A234742, A235035, A260735, A260720.
%K A260719 nonn
%O A260719 0,1
%A A260719 _Antti Karttunen_, Aug 04 2015