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).

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

1,2

Comments

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

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

Links

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

Index entries for sequences operating on GF(2)[X]-polynomials

Formula

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.

Prog

(PARI)
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)));

Crossrefs

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

Sequence in context: A048893 A330814 A305903 * A319345 A213651 A287796

Adjacent sequences: A305901 A305902 A305903 * A305905 A305906 A305907

Keyword

nonn

Author

Antti Karttunen, Jun 16 2018

Status

approved