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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. 8
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..7968

Index entries for sequences that are permutations of the natural numbers

FORMULA

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)).

PROG

(PARI)

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)));

CROSSREFS

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.

Sequence in context: A191730 A233560 A245703 * A167151 A273014 A072275

Adjacent sequences:  A260423 A260424 A260425 * A260427 A260428 A260429

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, Jul 26 2015

STATUS

approved

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)