A245816 - OEIS

A245816

Permutation of natural numbers induced when A245822 is restricted to nonprime numbers: a(n) = A062298(A245822(A018252(n))).

1, 2, 4, 5, 3, 10, 6, 22, 7, 16, 9, 23, 27, 51, 15, 17, 35, 13, 37, 11, 39, 56, 69, 38, 14, 18, 48, 78, 33, 120, 20, 19, 46, 67, 24, 62, 42, 34, 28, 73, 25, 103, 31, 206, 40, 55, 68, 92, 300, 26, 76, 50, 99, 65, 157, 281, 165, 184, 8, 121, 134, 277, 423, 30, 47, 36, 223, 70, 514, 75, 101, 116, 236, 139, 74

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OFFSET

1,2

COMMENTS

This permutation is induced when A245822 is restricted to nonprimes, A018252, the first column of A114537, but equally, when it is restricted to column 2 (A007821), column 3 (A049078), etc. of that square array, or alternatively, to the successive rows of A236542.

The sequence of fixed points f(n) begins as 1, 2, 15, 142, 548, 1694, 54681. A018252(f(n)) gives the nonprime terms of A245823.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A062298(A245822(A018252(n))).

As a composition of related permutations:

a(n) = A245820(A245814(n)).

Also following holds for all n >= 1:

a(n) = A062298(A049084(A245822(A007821(n)))).

a(n) = A062298(A049084(A049084(A245822(A049078(n))))).

etc.

PROG

(PARI)

allocatemem(123456789);

default(primelimit, 2^22)

A014580 = vector(2^18);

A091226 = vector(2^22);

A002808(n)={my(k); for(k=0, primepi(n), isprime(n++)&&k--); n}; \\ This function from M. F. Hasler, Oct 31 2008

A062298(n) = n-primepi(n);

A018252(n) = if(1==n, 1, A002808(n-1));

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, A091226[n] = A091226[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));

A245816(n) = A062298(A245822(A018252(n)));

for(n=1, 10001, write("b245816.txt", n, " ", A245816(n)));

(Scheme) (define (A245816 n) (A062298 (A245822 (A018252 n))))

CROSSREFS

Inverse: A245815.

Related permutations: A245814, A245820, A245822.

Cf. A007821, A018252, A049078, A062298, A114537, A236542, A245823.

Sequence in context: A269780 A038776 A210863 * A118461 A332667 A266408

Adjacent sequences: A245813 A245814 A245815 * A245817 A245818 A245819

KEYWORD

nonn

AUTHOR

Antti Karttunen, Aug 02 2014

STATUS

approved