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

Author

Antti Karttunen, Jul 25 2015

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A260424.

Related permutations: A245703, A246377, A260422, A260425.

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

Programs

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)))))))

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)).