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.

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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for sequences that are permutations of the natural numbers

Formula

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)).

Prog

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

Crossrefs

Inverse: A260424.

Related permutations: A245703, A246377, A260422, A260425.

Cf. A000040, A002808, A010051, A000720, A065855, A205783, A206074.

Sequence in context: A236850 A263028 A044921 * A193989 A321293 A246091

Adjacent sequences: A260420 A260421 A260422 * A260424 A260425 A260426

Keyword

nonn,look

Author

Antti Karttunen, Jul 25 2015

Status

approved