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

1,2

COMMENTS

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192

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) = 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)).

PROG

(PARI)

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)));

CROSSREFS

Inverse: A260423.

Related permutations: A245704, A246378, A260421, A260426.

Cf. A000040, A002808, A205783, A206074, A206075, A257000, A255572, A255574.

Sequence in context: A175427 A246098 A050608 * A046510 A090273 A135381

Adjacent sequences:  A260421 A260422 A260423 * A260425 A260426 A260427

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jul 25 2015

STATUS

approved

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Last modified January 20 11:11 EST 2020. Contains 331083 sequences. (Running on oeis4.)