A305901 - OEIS

%I #22 Jun 15 2018 09:26:38

%S 1,2,3,4,5,4,4,6,4,4,7,4,8,9,4,4,10,11,4,12,4,4,13,4,14,15,4,16,17,4,

%T 4,18,19,4,20,4,4,21,22,4,23,4,24,25,4,26,27,28,4,29,4,4,30,4,4,31,4,

%U 32,33,34,35,36,37,4,38,4,39,40,4,4,41,42,43,44,4,4,45,46,4,47,48,4,49,4,50,51,4,52,53,4,4,54,55,56,57,4,4,58,4,4,59,60,61

%N Filter sequence for all such sequences b, for which b(A006254(k)) = constant for all k >= 3.

%C Restricted growth sequence transform of A305900(A064216(n)).

%C For all i, j:

%C   a(i) = a(j) => A278223(i) = A278223(j).

%C   a(i) = a(j) => A253786(i) = A253786(j).

%H Antti Karttunen, <a href="/A305901/b305901.txt">Table of n, a(n) for n = 1..100000</a>

%F For n <= 3, a(n) = n, and for n >= 4, a(n) = 4 if 2n-1 is a prime (for all n in A006254[3..] = 4, 6, 7, 9, 10, 12, 15, ...), and for all other n (numbers n such that 2n-1 is composite), a(n) = running count from 5 onward.

%o (PARI)

%o up_to = 1000;

%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 v_partsums = partialsums(x -> isprime(x+x-1), up_to);

%o A305901(n) = if(n<=3,n,if(isprime(n+n-1),4,3+n-v_partsums[n]));

%Y Cf. A006254, A064216, A305900.

%Y Cf. also A305902.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 14 2018