A091226 -id:A091226 - cp's OEIS frontend

A246205 Permutation of natural numbers: a(1) = 1, a(A014580(n)) = A117968(a(n)), a(A091242(n)) = A117967(1+a(n)), where A117967 and A117968 give positive and negative parts of inverse of balanced ternary enumeration of integers, and A014580 resp. A091242 are the binary coded irreducible resp. reducible polynomials over GF(2).

1, 2, 7, 5, 3, 11, 23, 15, 4, 12, 22, 33, 6, 52, 17, 13, 35, 43, 25, 16, 137, 45, 53, 36, 58, 155, 29, 47, 462, 154, 66, 135, 37, 152, 426, 30, 8, 156, 1273, 428, 24, 148, 460, 41, 423, 1426, 71, 31, 9, 427, 4283, 1410, 34, 431, 75, 1274, 159, 1423, 21, 3707, 194, 99, 44, 10, 1412, 11115, 64, 3850, 38, 1404, 103, 4281, 26, 412, 3722, 49

Offset: 1

Antti Karttunen, Aug 19 2014

nonn

Inverse: A246206.
Similar or related entanglement permutations: A246163, A245701, A246201, A246207, A246209.
Cf. A014580, A091225, A091226, A091242, A091245, A117967, A117968.

a(1) = 1, and for n > 1, if A091225(n) = 1 [i.e. n is in A014580], a(n) = A117968(a(A091226(n))), otherwise a(n) = A117967(1+a(A091245(n))).
As a composition of related permutations:
a(n) = A246207(A245701(n)).
a(n) = A246209(A246201(n)).

A305817 Number of terms of A091206 <= n; Partial sums of A305816.

Original entry on oeis.org

0, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14

Offset: 1

Antti Karttunen, Jun 15 2018

nonn

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences operating on GF(2)[X]-polynomials

Cf. A000720, A091206, A091226, A235043, A235044, A305816.

up_to = 65537;
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];

a(1) = 0; for n > 1, a(n) = A305816(n-1) + a(n).

For all n >= 1, a(A091206(n)) = n.

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

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, 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

Antti Karttunen, Jun 14 2018

nonn

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).

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

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

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)));

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, ...).

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A305817 Number of terms of A091206 <= n; Partial sums of A305816.

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

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