A245815 Permutation of natural numbers induced when A245821 is restricted to nonprime numbers: a(n) = A062298(A245821(A018252(n))).

1, 2, 5, 3, 4, 7, 9, 59, 11, 6, 20, 125, 18, 25, 15, 10, 16, 26, 32, 31, 103, 8, 12, 35, 41, 50, 13, 39, 85, 64, 43, 164, 29, 38, 17, 66, 19, 24, 21, 45, 132, 37, 105, 139, 82, 33, 65, 27, 507, 52, 14, 180, 161, 96, 46, 22, 190, 141, 87, 1603, 80, 36, 143, 107, 54, 670, 34, 47, 23, 68, 177, 1337, 40

Offset

1,2

Comments

This permutation is induced when A245821 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(A245821(A018252(n))).

As a composition of related permutations:

a(n) = A245813(A245819(n)).

Also following holds for all n >= 1:

a(n) = A062298(A049084(A245821(A007821(n)))).

a(n) = A062298(A049084(A049084(A245821(A049078(n))))).

Prog

(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++);
A002808(n)={my(k); for(k=0, primepi(n), isprime(n++)&&k--); n}; \\ This function from M. F. Hasler
A062298(n) = n-primepi(n);
A018252(n) = if(1==n, 1, A002808(n-1));
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));
A245815(n) = A062298(A245821(A018252(n)));
for(n=1, 10001, write("b245815.txt", n, " ", A245815(n)));
(Scheme) (define (A245815 n) (A062298 (A245821 (A018252 n))))

Crossrefs

Inverse: A245816.

Related permutations: A245813, A245819, A245821.

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

Sequence in context: A357047 A105530 A370932 * A105108 A118460 A064788

Adjacent sequences: A245812 A245813 A245814 * A245816 A245817 A245818

Keyword

nonn

Author

Antti Karttunen, Aug 02 2014

Status

approved