A245821 Permutation of natural numbers: a(n) = A091205(A245703(n)).

1, 2, 3, 4, 5, 9, 7, 6, 8, 12, 11, 15, 23, 81, 18, 10, 17, 30, 13, 162, 27, 36, 19, 24, 16, 25, 38, 46, 37, 45, 31, 135, 14, 20, 50, 57, 47, 69, 21, 55, 83, 115, 419, 87, 60, 210, 61, 42, 54, 26, 90, 28, 29, 35, 32, 63, 171, 52, 59, 138, 113, 180, 111, 48, 88, 39, 41, 621, 72, 22, 953, 230, 103, 207, 126, 64, 33, 243

Offset: 1

Author

Antti Karttunen, Aug 02 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: A245822.

Other related permutations: A091205, A245703, A245815.

Fixed points: A245823.

Cf. A000040, A049084, A078442, A049076, A018252, A062298.

Programs

PARI

allocatemem(234567890);
v014580 = vector(2^18);
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++; v014580[i] = n; v091226[n] = v091226[n-1]+1, j++; v091242[j] = n; v091226[n] = v091226[n-1]); n++);
A014580(n) = v014580[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)}));
A245703(n) = if(1==n, 1, if(isprime(n), A014580(A245703(primepi(n))), A091242(A245703(n-primepi(n)-1))));
A245821(n) = A091205(A245703(n));
for(n=1, 10001, write("b245821.txt", n, " ", A245821(n)));

Scheme

(define (A245821 n) (A091205 (A245703 n)))

Formula

a(n) = A091205(A245703(n)).

Other identities. For all n >= 1, the following holds:

A078442(a(n)) = A078442(n), A049076(a(n)) = A049076(n). [Preserves "the order of primeness of n"].

a(p_n) = p_{a(n)} where p_n is the n-th prime, A000040(n).

a(n) = A049084(a(A000040(n))). [Thus the same permutation is induced also when it is restricted to primes].

A245815(n) = A062298(a(A018252(n))). [While restriction to nonprimes induces another permutation].