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A305811 Filter sequence for a(Fibonacci prime) = constant sequences.

%I A305811 #9 Jun 16 2018 18:30:35
%S A305811 1,2,2,3,2,4,5,6,7,8,9,10,2,11,12,13,14,15,16,17,18,19,20,21,22,23,24,
%T A305811 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,
%U A305811 48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,2,86,87,88,89,90
%N A305811 Filter sequence for a(Fibonacci prime) = constant sequences.
%C A305811 Restricted growth sequence transform of the ordered pair [A305800(n), A305820(n)].
%C A305811 For all i, j: a(i) = a(j) => A304105(i) = A304105(j).
%H A305811 Antti Karttunen, <a href="/A305811/b305811.txt">Table of n, a(n) for n = 1..100000</a>
%F A305811 a(1) = 1; for n > 1, if A010051(n)==1 and A010056(n)==1 [when n is a Fibonacci prime, A005478], a(n) = 2, otherwise a(n) = running count from 3 onward.
%o A305811 (PARI)
%o A305811 up_to = 100000;
%o A305811 A010056(n) = { my(k=n^2); k+=(k+1)<<2; (issquare(k) || (n>0 && issquare(k-8))) }; \\ From A010056
%o A305811 partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o A305811 v_partsums = partialsums(x -> (isprime(x)&&A010056(x)), up_to);
%o A305811 A305811(n) = if(1==n,n,if(isprime(n)&&A010056(n),2,1+n-v_partsums[n]));
%Y A305811 Cf. A005478, A010051, A010056, A304105, A305800, A305820.
%K A305811 nonn
%O A305811 1,2
%A A305811 _Antti Karttunen_, Jun 16 2018