A244987 Self-inverse permutation of natural numbers, A245703-conjugate of Blue code: a(n) = A245704(A193231(A245703(n))).

1, 3, 2, 6, 5, 4, 13, 8, 21, 15, 23, 16, 7, 25, 10, 12, 41, 18, 19, 64, 9, 22, 11, 49, 14, 26, 77, 39, 37, 34, 263, 105, 38, 30, 88, 70, 29, 33, 28, 133, 17, 54, 73, 126, 51, 462, 53, 60, 24, 66, 45, 74, 47, 42, 78, 94, 156, 81, 239, 48, 97, 62, 100, 20, 155, 50, 79, 98, 84, 36, 167, 141, 43, 52, 129, 164, 27, 55

Offset: 1

Author

Antti Karttunen, Aug 07 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

Cf. A000040, A002808, A010051, A193231, A245703, A245704, A234747, A234748, A245450, A245454.

Programs

PARI

allocatemem(234567890);
default(primelimit, 2^22);
A014580 = vector(2^18);
A091226 = vector(2^22);
A091242 = vector(2^22);
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++; A014580[i] = n; A091226[n] = A091226[n-1]+1, j++; A091242[j] = n; A091226[n] = A091226[n-1]); n++);
A091245(n) = ((n-A091226[n])-1);
A245703(n) = if(1==n, 1, if(isprime(n), A014580[A245703(primepi(n))], A091242[A245703(n-primepi(n)-1)]));
A245704(n) = if(1==n, 1, if(isA014580(n), prime(A245704(A091226[n])), A002808(A245704(A091245(n)))));
A193231(n) = {my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2)};
A244987(n) = A245704(A193231(A245703(n)));
for(n=1, 10001, write("b244987.txt", n, " ", A244987(n)));

Scheme

(define (A244987 n) (A245704 (A193231 (A245703 n))))

Formula

a(n) = A245704(A193231(A245703(n))).

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

A010051(a(n)) = A010051(n). [Maps primes to primes and composites to composites].