A305810 - OEIS

%I #13 Jun 16 2018 18:30:26

%S 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 25,26,5,27,28,29,30,31,32,33,34,35,36,37,5,38,39,40,41,42,43,44,45,

%U 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 Filter sequence for a(Sophie Germain primes > 3) = constant sequences.

%C Filer sequence for all such sequences S, for which S(A005384(k)) = constant for all k >= 3.

%C Restricted growth sequence transform of the ordered pair [A305900(n), A305901(1+n)].

%C For all i, j:

%C   a(i) = a(j) => A305900(i) = A305900(j),

%C   a(i) = a(j) => A305901(1+i) = A305901(1+j),

%C   a(i) = a(j) => A305978(i) = A305978(j),

%C   a(i) = a(j) => A305985(i) = A305985(j).

%H Antti Karttunen, <a href="/A305810/b305810.txt">Table of n, a(n) for n = 1..100000</a>

%F 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 (PARI)

%o up_to = 100000;

%o A156660(n) = (isprime(n)&&isprime(2*n+1)); \\ From A156660

%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 v156874 = partialsums(A156660, up_to);

%o A156874(n) = v156874[n];

%o A305810(n) = if(n<5,n,if(A156660(n),5,3+n-A156874(n)));

%Y Cf. A005384, A156660, A156874, A305900, A305901, A305978, A305985.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 16 2018