A245813 Permutation of natural numbers induced when A091205 is restricted to {1} and binary codes for polynomials reducible over GF(2): a(1) = 1, a(n) = A062298(A091205(A091242(n-1))).

1, 2, 5, 3, 4, 9, 11, 7, 6, 18, 10, 59, 20, 25, 16, 8, 50, 15, 32, 31, 12, 13, 38, 21, 41, 125, 85, 43, 17, 45, 52, 35, 22, 19, 103, 105, 33, 24, 14, 190, 68, 27, 66, 28, 161, 29, 80, 26, 54, 46, 177, 84, 258, 34, 180, 64, 90, 70, 507, 37, 196, 96, 39, 110, 430, 92, 78, 75, 600, 48, 40, 82, 213, 218, 71, 23, 87, 72, 51, 132, 30

Offset: 1

Author

Antti Karttunen, Aug 16 2014

Keywords

• nonn

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: A245814.

Cf. A062298, A091242.

Related permutations: A091205, A245815, A245820.

Programs

PARI

allocatemem(234567890);
v091226 = vector(2^22);
v091242 = vector(2^22);
isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
i=0; j=0; n=2; while((n < 2^22), if(isA014580(n), i++; v091226[n] = v091226[n-1]+1, j++; v091242[j] = n; v091226[n] = v091226[n-1]); n++);
A062298(n) = n-primepi(n);
A091226(n) = v091226[n];
A091242(n) = v091242[n];
A091205(n) = if(n<=1, n, if(isA014580(n), prime(A091205(A091226(n))), {my(irfs, t); irfs=subst(lift(factor(Mod(1, 2)*Pol(binary(n)))), x, 2); irfs[,1]=apply(t->A091205(t), irfs[,1]); factorback(irfs)}));
A245813(n) = if(n<=1, n, A062298(A091205(A091242(n-1))));
for(n=1, 10001, write("b245813.txt", n, " ", A245813(n)));

Scheme

(define (A245813 n) (if (<= n 1) n (A062298 (A091205 (A091242 (- n 1))))))

Formula

a(1) = 1, and for n > 1, a(n) = A062298(A091205(A091242(n-1))).

As a composition of related permutations:

a(n) = A245815(A245820(n)).