A245814 Permutation of natural numbers induced when A091204 is restricted to nonprime numbers: a(n) = 1+A091245(A091204(A018252(n))).

1, 2, 4, 5, 3, 9, 8, 16, 6, 11, 7, 21, 22, 39, 18, 15, 29, 10, 34, 13, 24, 33, 76, 38, 14, 48, 42, 44, 46, 81, 20, 19, 37, 54, 32, 92, 60, 23, 63, 71, 25, 99, 28, 233, 30, 50, 98, 70, 157, 17, 79, 31, 89, 49, 101, 191, 86, 91, 12, 161, 94, 171, 193, 56, 167, 43, 143, 41, 353, 58, 75, 78, 113, 102, 68, 190, 125, 67, 119, 47, 130, 72, 146, 52, 27

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: A245813.

Related permutations: A091204, A245816, A245819.

Cf. A018252, A091245.

Programs

PARI

allocatemem(123456789);
v014580 = vector(2^18);
v091226 = 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++; v091226[n] = v091226[n-1]); n++);
A002808(n)={my(k); for(k=0, primepi(n), isprime(n++)&&k--); n}; \\ This function from M. F. Hasler
A018252(n) = if(1==n, 1, A002808(n-1));
A014580(n) = v014580[n];
A091226(n) = v091226[n];
A091245(n) = ((n-A091226(n))-1);
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))}));
A245814(n) = 1 + A091245(A091204(A018252(n)))
for(n=1, 10001, write("b245814.txt", n, " ", A245814(n)));

Scheme

(define (A245814 n) (+ 1 (A091245 (A091204 (A018252 n)))))

Formula

a(n) = 1 + A091245(A091204(A018252(n))).

As a composition of related permutations:

a(n) = A245819(A245816(n)).