A305890 - OEIS

%I #7 Jul 01 2018 08:35:24

%S 1,2,3,4,3,5,3,6,7,8,3,9,3,10,11,12,3,13,3,14,15,16,3,17,18,19,20,21,

%T 3,22,3,23,24,25,26,27,3,28,29,30,3,31,3,32,33,34,3,35,36,37,38,39,3,

%U 40,41,42,43,44,3,45,3,46,47,48,49,50,3,51,52,53,3,54,3,55,56,57,58,59,3,60,61,62,3,63,64,65,66,67,3,68,69,70,71,72,73,74,3

%N Filter sequence for all such sequences b, for which b(A176997(k)) = constant for all k > 1, where A176997 is the union of odd primes and Fermat pseudoprimes.

%H Antti Karttunen, <a href="/A305890/b305890.txt">Table of n, a(n) for n = 1..101101</a>

%F For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A062173(i) = A062173(j).

%o (PARI)

%o up_to = 100000;

%o A257531(n) = if(n==1, 0, if(Mod(2, n)^(n-1)==1, 1, 0));

%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 vpartsums = partialsums(A257531, up_to);

%o Apartsums(n) = vpartsums[n];

%o A305890(n) = if(n<=2,n,if(A257531(n),3,1+n-Apartsums(n)));

%Y Cf. A001567, A062173, A176997, A257531.

%Y Differs from A305801 for the first time at n=341, where a(341) = 3, while A305801(341) = 275.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 01 2018