A305903 -id:A305903 - 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.

A305904 Filter sequence for all such sequences S, for which S(A091206(k)) = constant for all k >= 3, where A091206 gives primes whose binary representation encodes a polynomial irreducible over GF(2).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 7, 11, 7, 12, 13, 14, 15, 16, 7, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 7, 28, 29, 30, 31, 32, 7, 33, 34, 35, 7, 36, 37, 38, 39, 40, 7, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 7, 52, 7, 53, 54, 55, 56, 57, 7, 58, 59, 60, 61, 62, 7, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 7

Offset: 1

Antti Karttunen, Jun 16 2018

nonn

Restricted growth sequence transform of the ordered pair [A305900(n), A305903(n)].

For all i, j: a(i) = a(j) => A305815(i) = A305815(j).

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences operating on GF(2)[X]-polynomials

Cf. A091206, A305815, A305816, A305817, A305900, A305903.

up_to = 100000;
A305816(n) = (isprime(n)&&polisirreducible(Pol(binary(n))*Mod(1,2)));
partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
v305817 = partialsums(A305816, up_to);
A305817(n) = v305817[n];
A305904(n) = if(n<7,n,if(A305816(n),7,3+n-A305817(n)));

For n < 7, a(n) = n; for >= 7, a(n) = 7 if A305816(n) = 1 [when n is in A091206[3..] = 7, 11, 13, 19, 31, 37, 41, ...], and 3+n-A305817(n) otherwise.

cp's OEIS Frontend

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

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