A305903 Filter sequence for all such sequences b, for which b(A014580(k)) = constant for all k >= 3.

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

Offset

1,2

Comments

Restricted growth sequence transform of A305900(A091203(n)).

This is GF(2)[X] analog of A305900.

For all i, j:

a(i) = a(j) => A304529(i) = A304529(j) => A305788(i) = A305788(j).

a(i) = a(j) => A268389(i) = A268389(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 when n is in A014580[3..] (= 7, 11, 13, 19, 25, 31, ...), and a(n) = 3+n-A091226(n) when n is in A091242[4..] (= 8, 9, 10, 12, 14, 15, ...).

Prog

(PARI)
up_to = 1000;
A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
prepare_v091226(up_to) = { my(v = vector(up_to), c=0); for(i=1, up_to, c += A091225(i); v[i] = c); (v); }
v091226 = prepare_v091226(up_to);
A091226(n) = if(!n, n, v091226[n]);
A305903(n) = if(n<7, n, if(A091225(n), 7, 3+n-A091226(n)));

Crossrefs

Cf. A091203, A268389, A278233, A304529, A305788, A305900.

Sequence in context: A275987 A048893 A330814 * A305904 A319345 A213651

Adjacent sequences: A305900 A305901 A305902 * A305904 A305905 A305906

Keyword

nonn

Author

Antti Karttunen, Jun 14 2018

Status

approved