A305902 -id:A305902 - cp's OEIS frontend

A305900 Filter sequence for a(primes > 3) = constant sequences.

1, 2, 3, 4, 5, 6, 5, 7, 8, 9, 5, 10, 5, 11, 12, 13, 5, 14, 5, 15, 16, 17, 5, 18, 19, 20, 21, 22, 5, 23, 5, 24, 25, 26, 27, 28, 5, 29, 30, 31, 5, 32, 5, 33, 34, 35, 5, 36, 37, 38, 39, 40, 5, 41, 42, 43, 44, 45, 5, 46, 5, 47, 48, 49, 50, 51, 5, 52, 53, 54, 5, 55, 5, 56, 57, 58, 59, 60, 5, 61, 62, 63, 5, 64, 65, 66, 67, 68, 5, 69, 70, 71, 72, 73, 74, 75, 5, 76

Offset: 1

Antti Karttunen, Jun 14 2018

nonn

For all i, j:
  a(i) = a(j) => A305801(i) = A305801(j) => A305800(i) = A305800(j).
  a(i) = a(j) => A007949(i) = A007949(j).
  a(i) = a(j) => A305893(i) = A305893(j).

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

Cf. A305800, A305801, A305893.

Cf. also A305901, A305902, A305903 (this filter applied to various permutations of N).

A305900(n) = if(n<=5,n,if(isprime(n),5,3+n-primepi(n)));

For n <= 5, a(n) = n, for >= 5, a(n) = 5 when n is a prime, and a(n) = 3+n-A000720(n) when n is a composite.

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

Original entry on oeis.org

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

Antti Karttunen, Jun 14 2018

nonn

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).

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

Cf. A006254, A064216, A305900.

Cf. also A305902.

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]));

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.

cp's OEIS Frontend

A305900 Filter sequence for a(primes > 3) = constant sequences.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula