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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.
5
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
1,2
COMMENTS
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.
FORMULA
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)).
PROG
(PARI)
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)));
CROSSREFS
Inverse: A260421.
Related permutations: A246202, A246378, A260423, A260425.
Differs from A246378 for the first time at n=16, where a(16)=27, while A246378(16)=26.
Sequence in context: A213781 A257730 A246378 * A237126 A246380 A200639
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Jul 25 2015
STATUS
approved