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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. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..4244

Index entries for sequences that are permutations of the natural numbers

FORMULA

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)).

PROG

(PARI)

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)));

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

CROSSREFS

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.

Sequence in context: A083197 A235262 A245704 * A277905 A257802 A225850

Adjacent sequences:  A260422 A260423 A260424 * A260426 A260427 A260428

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 26 2015

STATUS

approved

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Last modified January 23 07:07 EST 2020. Contains 331168 sequences. (Running on oeis4.)