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A305903 Filter sequence for all such sequences b, for which b(A014580(k)) = constant for all k >= 3.

%I A305903 #12 Jun 15 2018 09:26:52
%S A305903 1,2,3,4,5,6,7,8,9,10,7,11,7,12,13,14,15,16,7,17,18,19,20,21,7,22,23,
%T A305903 24,25,26,7,27,28,29,30,31,7,32,33,34,7,35,36,37,38,39,7,40,41,42,43,
%U A305903 44,45,46,7,47,48,49,7,50,7,51,52,53,54,55,7,56,57,58,59,60,7,61,62,63,64,65,66,67,68,69,70,71,72,73,7,74,75,76,7,77,78,79,80,81,7
%N A305903 Filter sequence for all such sequences b, for which b(A014580(k)) = constant for all k >= 3.
%C A305903 Restricted growth sequence transform of A305900(A091203(n)).
%C A305903 This is GF(2)[X] analog of A305900.
%C A305903 For all i, j:
%C A305903   a(i) = a(j) => A304529(i) = A304529(j) => A305788(i) = A305788(j).
%C A305903   a(i) = a(j) => A268389(i) = A268389(j).
%H A305903 Antti Karttunen, <a href="/A305903/b305903.txt">Table of n, a(n) for n = 1..100000</a>
%H A305903 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A305903 For n < 7, a(n) = n, for >= 7, a(n) = 7 when n is in A014580[3..] (= 7, 11, 13, 19, 25, 31, ...), and a(n) = 3+n-A091226(n) when n is in A091242[4..] (= 8, 9, 10, 12, 14, 15, ...).
%o A305903 (PARI)
%o A305903 up_to = 1000;
%o A305903 A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
%o A305903 prepare_v091226(up_to) = { my(v = vector(up_to), c=0); for(i=1,up_to,c += A091225(i); v[i] = c); (v); }
%o A305903 v091226 = prepare_v091226(up_to);
%o A305903 A091226(n) = if(!n,n,v091226[n]);
%o A305903 A305903(n) = if(n<7,n,if(A091225(n),7,3+n-A091226(n)));
%Y A305903 Cf. A091203, A268389, A278233, A304529, A305788, A305900.
%K A305903 nonn
%O A305903 1,2
%A A305903 _Antti Karttunen_, Jun 14 2018