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A305894 Filter sequence for a(Sophie Germain primes) = constant sequences.

%I A305894 #6 Jul 01 2018 08:35:31
%S A305894 1,2,2,3,2,4,5,6,7,8,2,9,10,11,12,13,14,15,16,17,18,19,2,20,21,22,23,
%T A305894 24,2,25,26,27,28,29,30,31,32,33,34,35,2,36,37,38,39,40,41,42,43,44,
%U A305894 45,46,2,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,2,76,77,78,79,80,2,81
%N A305894 Filter sequence for a(Sophie Germain primes) = constant sequences.
%C A305894 For all i, j:
%C A305894   a(i) = a(j) => A305800(i) = A305800(j),
%C A305894   a(i) = a(j) => A305978(i) = A305978(j).
%H A305894 Antti Karttunen, <a href="/A305894/b305894.txt">Table of n, a(n) for n = 1..100000</a>
%F A305894 a(1) = 1; for n > 1, a(n) = 2 if A156660(n) == 1 [when n is in A005384 = 2, 3, 5, 11, 23, 29, 41, 53, 83, 89, 113, ...], otherwise a(n) = 1+n-A156874(n).
%o A305894 (PARI)
%o A305894 up_to = 100000;
%o A305894 A156660(n) = (isprime(n)&&isprime(2*n+1)); \\ From A156660
%o A305894 partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o A305894 v156874 = partialsums(A156660, up_to);
%o A305894 A156874(n) = v156874[n];
%o A305894 A305894(n) = if(n<2,n,if(A156660(n),2,1+n-A156874(n)));
%Y A305894 Cf. A005384, A156660, A156874, A305800, A305810, A305978.
%K A305894 nonn
%O A305894 1,2
%A A305894 _Antti Karttunen_, Jul 01 2018