A205783 -id:A205783 - cp's OEIS frontend

A260426 a(1) = 1, a(A206074(n)) = A014580(a(n)), a(A205783(1+n)) = A091242(a(n)), where A014580 [respectively A091242] give binary codes for irreducible [resp. reducible] polynomials over GF(2), while A206074 and A205783 give similar codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

1, 2, 3, 4, 7, 5, 11, 6, 8, 12, 25, 9, 13, 17, 10, 14, 47, 18, 19, 34, 15, 20, 31, 24, 55, 16, 21, 62, 137, 26, 37, 27, 45, 22, 28, 42, 59, 33, 71, 23, 87, 29, 41, 79, 166, 35, 61, 49, 36, 58, 30, 38, 319, 54, 91, 76, 44, 89, 97, 32, 203, 108, 39, 53, 99, 200, 67, 46, 103, 78, 185, 64, 131, 48, 75, 40, 379, 50, 73, 373, 109, 70, 433, 113, 95, 57, 1123, 111, 143, 121

Offset: 1

Antti Karttunen, Jul 26 2015

Each term of A260427 resides in a separate infinite cycle. This follows because any polynomial with (coefficients 0 or 1) that is irreducible over GF(2) is also irreducible over Q, in other words, A014580 is a subset of A206074. [See Thomas Ordowski's Feb 21 2014 comment in A014580] and thus any term of A091242 in A206074 is trapped into a trajectory containing only terms of A014580.

Antti Karttunen, Table of n, a(n) for n = 1..7968
Index entries for sequences that are permutations of the natural numbers

Inverse: A260425.
Related permutations: A246202, A245703, A260421, A260424.
Cf. A014580, A091242, A205783, A206074, A257000, A255572, A255574, A260427.
Differs from A245703 for the first time at n=25, where a(25)=55, while A245703(25)=16.

allocatemem(234567890);
vecsize = (2^24)-4;
uplim = 2^25;
v014580 = vector(vecsize); A014580 = n -> v014580[n];
v091242 = vector(vecsize); A091242 = n -> v091242[n];
v255574 = vector(vecsize); A255574 = n -> v255574[n];
A255572 = n -> (n - A255574(n) - 1);
isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
isA206074(n) = polisirreducible(Pol(binary(n)));
A257000 = n -> isA206074(n);
v255574[1] = 0; i=0; j=0; n=2; while((n < uplim), if(!(n%65536),print1(n,", ")); v255574[n] = v255574[n-1]+A257000(n); if(isA014580(n), i++; v014580[i] = n, j++; v091242[j] = n); n++); print(n);
A260426(n) = if(1==n, 1, if(isA206074(n), A014580(A260426(A255574(n))), A091242(A260426(A255572(n)))));
for(n=1, 7968, write("b260426.txt", n, " ", A260426(n)));

a(1) = 1; for n > 1, if A257000(n) = 1 [when n is in A206074], then a(n) = A014580(a(A255574(n))), otherwise [when n is in A205783], a(n) = A091242(a(A255572(n))).
As a composition of related permutations:
a(n) = A246202(A260421(n)).
a(n) = A245703(A260424(n)).

A255572 a(n) = Number of terms larger than one in range 0 .. n of A205783.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 2, 2, 3, 4, 5, 5, 6, 6, 7, 8, 9, 9, 10, 10, 11, 12, 13, 13, 14, 14, 15, 16, 17, 17, 18, 18, 19, 20, 21, 22, 23, 23, 24, 25, 26, 26, 27, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 35, 36, 36, 37, 38, 39, 39, 40, 40, 41, 42, 43, 44, 45, 45, 46, 46, 47, 47, 48, 48, 49, 50, 51, 51, 52, 52, 53, 53

Offset: 0

Antti Karttunen, May 14 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Essentially one less than A255573 (after the initial zero).

Cf. A065855, A091245, A205783, A255574.

A255572_write_bfile(up_to_n) = { my(n,a_n=0); for(n=0, up_to_n, if(((n > 1) && !polisirreducible(Pol(binary(n)))),a_n++); write("b255572.txt", n, " ", a_n)); };
A255572_write_bfile(8192);

Other identities and observations. For all n >= 1:
a(n) = A255573(n) - 1.
a(n) <= A065855(n).
a(n) <= A091245(n).

A260421 a(1) = 1, a(A206074(n)) = 1 + (2a(n)), a(A205783(1+n)) = 2a(n), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

Original entry on oeis.org

1, 3, 7, 2, 15, 6, 5, 14, 4, 30, 31, 12, 13, 10, 28, 8, 11, 60, 29, 62, 24, 26, 9, 20, 61, 56, 16, 22, 63, 120, 25, 58, 124, 48, 52, 18, 27, 40, 122, 112, 21, 32, 57, 44, 126, 240, 17, 50, 116, 248, 96, 104, 23, 36, 121, 54, 80, 244, 59, 224, 125, 42, 64, 114, 88, 252, 49, 480, 53, 34, 19, 100, 41, 232, 496, 192, 123, 208, 113, 46, 33, 72, 45

Offset: 1

Antti Karttunen, Jul 25 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A260422.
Related permutations: A246201, A246377, A260424, A260426.
Cf. A257000, A255572, A255574.

allocatemem(123456789);
uplim = 2^20;
v255574 = vector(uplim); A255574 = n -> v255574[n];
A255572 = n -> (n - A255574(n) - 1);
isA206074(n) = polisirreducible(Pol(binary(n)));
v255574[1] = 0; i=0; j=0; n=2; while((n < uplim), v255574[n] = v255574[n-1]+isA206074(n); n++);
A260421(n) = if(1==n, 1, if(isA206074(n), 1 + 2*(A260421(A255574(n))), 2*(A260421(A255572(n)))));
for(n=1, 8192, write("b260421.txt", n, " ", A260421(n)));

If A257000(n) = 1 [when n is one of the terms of A206074] then a(n) = 1 + 2*a(A255574(n)), otherwise a(n) = 2*A260421(A255572(n)).
As a composition of related permutations:
a(n) = A246377(A260424(n)).
a(n) = A246201(A260426(n)).

A260422 a(1) = 1, a(2n) = A205783(1+a(n)), a(2n+1) = A206074(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

Original entry on oeis.org

1, 4, 2, 9, 7, 6, 3, 16, 23, 14, 17, 12, 13, 8, 5, 27, 47, 36, 71, 24, 41, 28, 53, 21, 31, 22, 37, 15, 19, 10, 11, 42, 81, 70, 149, 54, 109, 106, 239, 38, 73, 62, 127, 44, 83, 80, 171, 34, 67, 48, 91, 35, 69, 56, 113, 26, 43, 32, 59, 18, 25, 20, 29, 63, 131, 122, 271, 105, 233, 216, 477, 82, 173, 159, 353, 155, 347, 345, 787, 57

Offset: 1

Antti Karttunen, Jul 25 2015

This sequence can be represented as a binary tree. Each left hand child is produced as A205783(1+n), and each right hand child as A206074(n), when the parent contains n:
                                     |
                  ...................1...................
                 4                                       2
       9......../ \........7                   6......../ \........3
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  16       23         14       17         12       13          8       5
27  47   36  71     24  41   28  53     21  31   22  37      15 19   10 11
etc.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A260421.
Related permutations: A246202, A246378, A260423, A260425.
Cf. A205783, A206074.
Differs from A246378 for the first time at n=16, where a(16)=27, while A246378(16)=26.

uplim = (2^21) + (2^20);
v206074 = vector(uplim);
v205783 = vector(uplim); v205783[1] = 1;
isA206074(n) = polisirreducible(Pol(binary(n)));
i=0; j=1; n=2; while((n < uplim), if(!(n%65536),print1(n,", "));  if(isA206074(n), i++; v206074[i] = n, j++; v205783[j] = n); n++); print(n);
A260422(n) = if(1==n, 1, if(0==(n%2), v205783[1+A260422(n/2)], v206074[A260422((n-1)/2)]));
for(n=1, 8192, write("b260422.txt", n, " ", A260422(n)));

a(1) = 1, a(2n) = A205783(1+a(n)), a(2n+1) = A206074(a(n)).
As a composition of related permutations:
a(n) = A260423(A246378(n)).
a(n) = A260425(A246202(n)).

A255573 a(n) = Number of terms of A205783 (including 1) in range 0 .. n.

Original entry on oeis.org

0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, 11, 12, 13, 14, 14, 15, 15, 16, 17, 18, 18, 19, 19, 20, 21, 22, 23, 24, 24, 25, 26, 27, 27, 28, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 36, 37, 37, 38, 39, 40, 40, 41, 41, 42, 43, 44, 45, 46, 46, 47, 47, 48, 48, 49, 49, 50, 51, 52, 52

Offset: 0

Antti Karttunen, May 14 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Essentially one more than A255572 (after the initial zero).

Cf. A062298, A205783, A255574.

A255573_write_bfile(up_to_n) = { my(n,a_n=0); for(n=0, up_to_n, if(((n > 0) && !polisirreducible(Pol(binary(n)))),a_n++); write("b255573.txt", n, " ", a_n)); };
A255573_write_bfile(8192);

a(n) = n - A255574(n).
Other identities and observations. For all n >= 1:
a(n) = 1 + A255572(n).
a(n) <= A062298(n).

A260423 a(1) = 1, a(prime(n)) = A206074(a(n)), a(composite(n)) = A205783(1+a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 30, 25, 32, 29, 33, 34, 35, 36, 38, 31, 40, 42, 44, 37, 46, 41, 39, 49, 45, 43, 50, 51, 52, 54, 57, 47, 48, 60, 63, 65, 56, 53, 68, 55, 62, 58, 74, 66, 64, 59, 75, 76, 78, 61, 82, 67, 86, 70, 72, 92, 95, 69, 98, 85, 80, 71, 102, 84, 94, 88, 111

Offset: 1

Antti Karttunen, Jul 25 2015

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A260424.
Related permutations: A245703, A246377, A260422, A260425.
Cf. A000040, A002808, A010051, A000720, A065855, A205783, A206074.

allocatemem(123456789);
default(primelimit,4294965247);
uplim = 2^23;
v206074 = vector(uplim); A206074 = n -> v206074[n];
v205783 = vector(uplim); A205783 = n -> v205783[n];
isA206074(n) = polisirreducible(Pol(binary(n)));
v205783[1] = 1; i=0; j=1; n=2; while((n < uplim), if(!(n%65536),print1(n,", ")); if(isA206074(n), i++; v206074[i] = n, j++; v205783[j] = n); n++); print(n);
A260423(n) = if(1==n, 1, if(isprime(n), A206074(A260423(primepi(n))), A205783(1+A260423(n-primepi(n)-1))));
for(n=1, 10001, write("b260423.txt", n, " ", A260423(n)));

(definec (A260423 n) (cond ((<= n 1) n) ((= 1 (A010051 n)) (A206074 (A260423 (A000720 n)))) (else (A205783 (+ 1 (A260423 (A065855 n)))))))

a(1) = 1; for n > 1, if A010051(n) = 1 [when n is a prime], then a(n) = A206074(a(A000720(n))), otherwise [when n is a composite], a(n) = A205783(1+a(A065855(n))).
As a composition of related permutations:
a(n) = A260422(A246377(n)).
a(n) = A260425(A245703(n)).

A260424 a(1) = 1, a(A206074(n)) = prime(a(n)), a(A205783(1+n)) = composite(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 29, 25, 26, 27, 31, 28, 37, 30, 32, 33, 34, 35, 41, 36, 44, 38, 43, 39, 47, 40, 46, 42, 53, 54, 45, 48, 49, 50, 59, 51, 61, 58, 52, 63, 67, 55, 71, 62, 56, 66, 57, 65, 73, 60, 79, 75, 83, 76, 89, 64, 68, 69, 109, 70, 97, 82, 101, 72, 103, 85, 81, 74, 127

Offset: 1

Antti Karttunen, Jul 25 2015

nonn

After 1, each term of A206075 resides in a separate infinite cycle. This follows because primes (A000040) is a subsequence of A206074 [see Thomas Ordowski's Feb 19 2014 comment in A206074] and thus each composite in A206074 is trapped into a trajectory containing only primes.

Antti Karttunen, Table of n, a(n) for n = 1..8192
Index entries for sequences that are permutations of the natural numbers

Inverse: A260423.
Related permutations: A245704, A246378, A260421, A260426.
Cf. A000040, A002808, A205783, A206074, A206075, A257000, A255572, A255574.

allocatemem(123456789);
default(primelimit,4294965247);
uplim = 2^20;
v255574 = vector(uplim); A255574 = n -> v255574[n];
A255572 = n -> (n - A255574(n) - 1);
A257000(n) = polisirreducible(Pol(binary(n)));
v255574[1] = 0; i=0; j=0; n=2; while((n < uplim), v255574[n] = v255574[n-1]+A257000(n); n++);
A002808(n)={ my(k=-1); while( -n + n += -k + k=primepi(n), ); n}; \\ This function from M. F. Hasler
A260424(n) = if(1==n, 1, if(A257000(n), prime(A260424(A255574(n))), A002808(A260424(A255572(n)))));
for(n=1, 8192, write("b260424.txt", n, " ", A260424(n)));

a(1) = 1; for n > 1, if A257000(n) = 1 [when n is in A206074], then a(n) = A000040(a(A255574(n))), otherwise [when n is in A205783], a(n) = A002808(a(A255572(n))).
As a composition of related permutations:
a(n) = A246378(A260421(n)).
a(n) = A245704(A260426(n)).

A260425 a(1) = 1, a(A014580(n)) = A206074(a(n)), a(A091242(n)) = A205783(1+a(n)), where A014580(n) [resp. A091242(n)] give binary codes for n-th irreducible [resp. reducible] polynomial over GF(2), while A206074 and A205783 give similar codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 5, 9, 12, 15, 7, 10, 13, 16, 21, 26, 14, 18, 19, 22, 27, 34, 40, 24, 11, 30, 32, 35, 42, 51, 23, 60, 38, 20, 46, 49, 31, 52, 63, 76, 43, 36, 92, 57, 33, 68, 17, 74, 48, 78, 95, 114, 64, 54, 25, 135, 86, 50, 37, 102, 47, 28, 111, 72, 118, 140, 67, 165, 96, 82, 39, 195, 79, 128, 75, 56, 150, 70, 44

Offset: 1

Antti Karttunen, Jul 26 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..4244
Index entries for sequences that are permutations of the natural numbers

Inverse: A260426.
Related permutations: A246201, A245704, A260422, A260423.
Cf. A014580, A091225, A091226, A091242, A091245, A205783, A206074.
Differs from A245704 for the first time at n=16, where a(16) = 26, while A245704(16) = 25.

allocatemem(234567890);
vecsize = (2^24)-4;
uplim = 2^25;
v091226 = vector(vecsize); A091226 = n -> v091226[n];
A091245(n) = ((n-A091226(n))-1);
v206074 = vector(vecsize); A206074 = n -> v206074[n];
v205783 = vector(vecsize); A205783 = n -> v205783[n];
isA014580(n) = polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
isA206074(n) = polisirreducible(Pol(binary(n)));
v091226[1] = 0; v205783[1] = 1; i=0; j=1; n=2; while((n < uplim), if(!(n%65536),print1(n,", ")); if(isA206074(n), i++; v206074[i] = n, j++; v205783[j] = n); if(isA014580(n), v091226[n] = v091226[n-1]+1, v091226[n] = v091226[n-1]); n++); print(n);
A260425(n) = if(1==n, 1, if(isA014580(n), A206074(A260425(A091226(n))), A205783(1+A260425(A091245(n)))));
for(n=1, 4244, write("b260425.txt", n, " ", A260425(n)));

(definec (A260425 n) (cond ((<= n 1) n) ((= 1 (A091225 n)) (A206074 (A260425 (A091226 n)))) (else (A205783 (+ 1 (A260425 (A091245 n)))))))

a(1) = 1; for n > 1, if A091225(n) = 1 [when n is in A014580], then a(n) = A206074(a(A091226(n))), otherwise [when n is in A091242], a(n) = A205783(1+a(A091245(n))).
As a composition of related permutations:
a(n) = A260422(A246201(n)).
a(n) = A260423(A245704(n)).

A206074 n-th irreducible polynomial over Q (with coefficients 0 or 1) evaluated at x=2.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 37, 41, 43, 47, 53, 55, 59, 61, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 97, 101, 103, 107, 109, 113, 115, 117, 121, 127, 131, 137, 139, 143, 145, 149, 151, 157, 163, 167, 169, 171, 173, 179, 181, 185, 191, 193, 197, 199, 203, 205, 209, 211, 213, 223, 227, 229

Offset: 1

Clark Kimberling, Feb 03 2012

nonn

Is every prime present?
Yes, see the Filaseta reference. - Thomas Ordowski, Feb 19 2014
Corresponding evaluation at x=10 is A206073. - Michael Somos, Feb 26 2014

			(See the example at A206073.)

Antti Karttunen, Table of n, a(n) for n = 1..21692
John Brillhart, Michael Filaseta, Andrew Odlyzko, On an irreducibility theorem of A. Cohn, Canad. J. Math. 33(1981), pp. 1055-1059.
Michael Filaseta, A further generalization of an irreducibility theorem of A. Cohn, Canad J. Math. 34 (1982), pp. 1390-1395.

Cf. A206073, A205783 (complement), A206075 (nonprime terms), A014580 (irreducible over GF(2), a subsequence of this one), A000040 (primes, also a subsequence), A260427 (terms that are reducible over GF(2)).
Cf. A255574 (left inverse).
Cf. also permutations A260421 - A260426.
Disjoint union of A257688 (without 1) and A260428.
a(n) differs from A186891(n+1) for the first time at n=21, where a(21) = 67, while A186891(22) = 65, a term missing from here. There are several other sequences that do not diverge until after approx. the twentieth term from this one (see the context-links).

t = Table[IntegerDigits[n, 2], {n, 1, 850}];
b[n_] := Reverse[Table[x^k, {k, 0, n}]]
p[n_, x_] := t[[n]].b[-1 + Length[t[[n]]]]
Table[p[n, x], {n, 1, 15}]
u = {}; Do[n++; If[IrreduciblePolynomialQ[p[n, x]],
AppendTo[u, n]], {n, 300}];
u                          (* A206074 *)
Complement[Range[200], u]  (* A205783 *)
b[n_] := FromDigits[IntegerDigits[u, 2][[n]]]
Table[b[n], {n, 1, 40}]    (* A206073 *)

for(n=2, 10^3, if( polisirreducible( Pol(binary(n)) ), print1(n,", ") ) ); \\ Joerg Arndt, Feb 19 2014

Other identities and observations. For all n >= 1:

A255574(a(n)) = n.

Clarified name, added more terms, Joerg Arndt, Feb 20 2014

A175526 A000120-abundant numbers.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 115, 116, 117, 118, 120

Offset: 1

Vladimir Shevelev, Dec 03 2010

nonn

Definition see in A175522. All even numbers > 2 are in the sequence.

A192895(a(n)) > 0. Reinhard Zumkeller, Jul 12 2011

Reinhard Zumkeller (first 1000 terms) & Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A175522 (perfect version), A175524 (deficient version), A257691 (complement, non-abundant version).
Cf. A000120, A192895.
Cf. also A005100, A005101.
a(n) differs from A091212(n) and from A205783(n+1) for the first time at n=37, where a(37) = 55, while 55 is missing from both A091212 and A205783.
Differs from A192506 for the first time at n=54, where a(54) = 77, while 77 is missing from A192506.

import Data.List (findIndices)
a175526 n = a175526_list !! (n-1)
a175526_list = map (+ 1) $ findIndices (> 0) a192895_list
-- Reinhard Zumkeller, Jul 12 2011

isA175526 := proc(n) s := 0 ; for d in (numtheory[divisors](n) minus {n}) do s := s+A000120(d) ; end do: evalb(s> A000120(n)) ; end proc:
for n from 1 to 120 do if isA175526(n) then printf("%d,",n); end if; end do: # R. J. Mathar, Jul 11 2011

okQ[n_] := DivisorSum[n, Total[IntegerDigits[#, 2]]*(-1)^Boole[#==n]&]>0; Select[Range[120], okQ] (* Jean-François Alcover, Dec 06 2015 *)

A192895(n) = sumdiv(n, d, hammingweight(d)*(-1)^(d==n)); \\ Charles R Greathouse IV, Feb 07 2013
isA175526(n) = (A192895(n) > 0);
n = 0; i = 0; while(i < 10000, n++; if(isA175526(n), i++; write("b175526.txt", i, " ", n)));
\\ Antti Karttunen, May 11 2015

is(n)=sumdiv(n,d,hammingweight(d))>2*hammingweight(n) \\ Charles R Greathouse IV, Jan 28 2016

is_A175526 = lambda x: sum(A000120(d) for d in divisors(x)) > 2*A000120(x)
A175526 = filter(is_A175526, IntegerRange(1, 10**4))
# D. S. McNeil, Dec 04 2010

cp's OEIS Frontend

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A255572 a(n) = Number of terms larger than one in range 0 .. n of A205783.

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A260421 a(1) = 1, a(A206074(n)) = 1 + (2*a(n)), a(A205783(1+n)) = 2*a(n), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

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A260422 a(1) = 1, a(2n) = A205783(1+a(n)), a(2n+1) = A206074(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

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A255573 a(n) = Number of terms of A205783 (including 1) in range 0 .. n.

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A260423 a(1) = 1, a(prime(n)) = A206074(a(n)), a(composite(n)) = A205783(1+a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

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A260424 a(1) = 1, a(A206074(n)) = prime(a(n)), a(A205783(1+n)) = composite(a(n)), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.

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A206074 n-th irreducible polynomial over Q (with coefficients 0 or 1) evaluated at x=2.

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A260421 a(1) = 1, a(A206074(n)) = 1 + (2a(n)), a(A205783(1+n)) = 2a(n), where A206074 and A205783 give binary codes for polynomials with coefficients 0 or 1 that are irreducible [resp. reducible] over Q.