%I #11 Jun 16 2018 18:30:59
%S 1,2,3,4,5,6,7,8,9,10,7,11,7,12,13,14,15,16,7,17,18,19,20,21,22,23,24,
%T 25,26,27,7,28,29,30,31,32,7,33,34,35,7,36,37,38,39,40,7,41,42,43,44,
%U 45,46,47,48,49,50,51,7,52,7,53,54,55,56,57,7,58,59,60,61,62,7,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,7
%N Filter sequence for all such sequences S, for which S(A091206(k)) = constant for all k >= 3, where A091206 gives primes whose binary representation encodes a polynomial irreducible over GF(2).
%C Restricted growth sequence transform of the ordered pair [A305900(n), A305903(n)].
%C For all i, j: a(i) = a(j) => A305815(i) = A305815(j).
%H Antti Karttunen, <a href="/A305904/b305904.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F For n < 7, a(n) = n; for >= 7, a(n) = 7 if A305816(n) = 1 [when n is in A091206[3..] = 7, 11, 13, 19, 31, 37, 41, ...], and 3+n-A305817(n) otherwise.
%o (PARI)
%o up_to = 100000;
%o A305816(n) = (isprime(n)&&polisirreducible(Pol(binary(n))*Mod(1,2)));
%o partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o v305817 = partialsums(A305816, up_to);
%o A305817(n) = v305817[n];
%o A305904(n) = if(n<7,n,if(A305816(n),7,3+n-A305817(n)));
%Y Cf. A091206, A305815, A305816, A305817, A305900, A305903.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jun 16 2018