A305901 Filter sequence for all such sequences b, for which b(A006254(k)) = constant for all k >= 3.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jun 14 2018

Keywords

• nonn

Comments

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

For all i, j:

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

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A006254, A064216, A305900.

Cf. also A305902.

Programs

PARI

up_to = 1000;
partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
v_partsums = partialsums(x -> isprime(x+x-1), up_to);
A305901(n) = if(n<=3,n,if(isprime(n+n-1),4,3+n-v_partsums[n]));

Formula

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.