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%I A305810 #13 Jun 16 2018 18:30:26
%S A305810 1,2,3,4,5,6,7,8,9,10,5,11,12,13,14,15,16,17,18,19,20,21,5,22,23,24,
%T A305810 25,26,5,27,28,29,30,31,32,33,34,35,36,37,5,38,39,40,41,42,43,44,45,
%U A305810 46,47,48,5,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,5,78,79,80,81,82,5,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,5
%N A305810 Filter sequence for a(Sophie Germain primes > 3) = constant sequences.
%C A305810 Filer sequence for all such sequences S, for which S(A005384(k)) = constant for all k >= 3.
%C A305810 Restricted growth sequence transform of the ordered pair [A305900(n), A305901(1+n)].
%C A305810 For all i, j:
%C A305810   a(i) = a(j) => A305900(i) = A305900(j),
%C A305810   a(i) = a(j) => A305901(1+i) = A305901(1+j),
%C A305810   a(i) = a(j) => A305978(i) = A305978(j),
%C A305810   a(i) = a(j) => A305985(i) = A305985(j).
%H A305810 Antti Karttunen, <a href="/A305810/b305810.txt">Table of n, a(n) for n = 1..100000</a>
%F A305810 If n < 5, a(n) = n; for n >= 5, a(n) = 5 if A156660(n) == 1 [when n is in A005384[3..] = 5, 11, 23, 29, 41, 53, 83, 89, 113, ...], otherwise a(n) = 3+n-A156874(n).
%o A305810 (PARI)
%o A305810 up_to = 100000;
%o A305810 A156660(n) = (isprime(n)&&isprime(2*n+1)); \\ From A156660
%o A305810 partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o A305810 v156874 = partialsums(A156660, up_to);
%o A305810 A156874(n) = v156874[n];
%o A305810 A305810(n) = if(n<5,n,if(A156660(n),5,3+n-A156874(n)));
%Y A305810 Cf. A005384, A156660, A156874, A305900, A305901, A305978, A305985.
%K A305810 nonn
%O A305810 1,2
%A A305810 _Antti Karttunen_, Jun 16 2018

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