A245822 Permutation of natural numbers: a(n) = A245704(A091204(n)).

1, 2, 3, 4, 5, 8, 7, 9, 6, 16, 11, 10, 19, 33, 12, 25, 17, 15, 23, 34, 39, 70, 13, 24, 26, 50, 21, 52, 53, 18, 31, 55, 77, 93, 54, 22, 29, 27, 66, 105, 67, 48, 137, 156, 30, 28, 37, 64, 91, 35, 85, 58, 97, 49, 40, 98, 36, 135, 59, 45, 47, 261, 56, 76, 92, 122, 83, 374, 38, 102, 139, 69, 167, 130, 88, 203, 351, 212, 349, 235, 14

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: A245821.

Other related permutations: A091204, A245704, A245816.

Fixed points: A245823.

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

Programs

PARI

allocatemem(123456789);
default(primelimit, 2^22)
v014580 = vector(2^18); A014580(n) = v014580[n];
v091226 = vector(2^22); A091226(n) = v091226[n];
A002808(n)={ my(k=-1); while( -n + n += -k + k=primepi(n), ); n}; \\ This function from M. F. Hasler
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, v091226[n] = v091226[n-1]); n++)
A091204(n) = if(n<=1, n, if(isprime(n), A014580(A091204(primepi(n))), {my(pfs, t, bits, i); pfs=factor(n); pfs[,1]=apply(t->Pol(binary(A091204(t))), pfs[,1]); sum(i=1, #bits=Vec(factorback(pfs))%2, bits[i]<<(#bits-i))}));
A091245(n) = ((n-A091226(n))-1);
A245704(n) = if(1==n, 1, if(isA014580(n), prime(A245704(A091226(n))), A002808(A245704(A091245(n)))));
A245822(n) = A245704(A091204(n));
for(n=1, 10001, write("b245822.txt", n, " ", A245822(n)));

Scheme

(define (A245822 n) (A245704 (A091204 n)))

Formula

a(n) = A245704(A091204(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].

A245816(n) = A062298(a(A018252(n))). [While restriction to nonprimes induces another permutation].