A245819 -id:A245819 - cp's OEIS frontend

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

Antti Karttunen, Aug 16 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A245813.
Related permutations: A091204, A245816, A245819.
Cf. A018252, A091245.

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)));

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

a(n) = 1 + A091245(A091204(A018252(n))).
As a composition of related permutations:
a(n) = A245819(A245816(n)).

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

Original entry on oeis.org

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

Antti Karttunen, Aug 02 2014

nonn

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.

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A245816.
Related permutations: A245813, A245819, A245821.
Cf. A007821, A018252, A049078, A062298, A114537, A236542, A245823.

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)));

(define (A245815 n) (A062298 (A245821 (A018252 n))))

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))))).

A245820 Permutation of natural numbers induced when A245704 is restricted to {1} and binary codes for polynomials reducible over GF(2): a(1) = 1, a(n) = A062298(A245704(A091242(n-1))).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 9, 6, 10, 13, 16, 8, 11, 14, 17, 22, 26, 15, 19, 20, 23, 27, 34, 39, 25, 12, 29, 31, 35, 40, 50, 24, 56, 37, 21, 43, 46, 38, 51, 57, 70, 48, 36, 78, 53, 33, 61, 18, 65, 55, 71, 79, 95, 67, 52, 30, 106, 75, 49, 42, 85, 54, 28, 89, 77, 96, 107, 74, 126, 92, 73, 45, 141, 98, 101, 69, 59, 116, 76, 41, 120, 105

Offset: 1

Antti Karttunen, Aug 16 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A245819.
Related permutations: A245704, A245813, A245816.
Cf. A014580, A036234, A062298, A091242.

\\ The rest of code can be found in A245704.
A245820(n) = if(1==n, 1, 1 + A245704(n-1));

(define (A245820 n) (if (<= n 1) n (+ 1 (A245704 (- n 1)))))

(define (A245820 n) (if (<= n 1) n (A062298 (A245704 (A091242 (- n 1))))))

(define (A245820 n) (if (<= n 1) n (A036234 (A245704 (A014580 (- n 1))))))

a(1) = 1, and for n > 1, a(n) = 1 + A245704(n-1).
a(1) = 1, and for n > 1, a(n) = A062298(A245704(A091242(n-1))). [Induced when A245704 is restricted to {1} and binary codes for polynomials reducible over GF(2)].
a(1) = 1, and for n > 1, a(n) = A036234(A245704(A014580(n-1))). [Induced also when A245703 is restricted to {1} and other binary codes for polynomials not reducible over GF(2)].
As a composition of related permutations:
a(n) = A245816(A245813(n)).

cp's OEIS Frontend

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

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

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A245820 Permutation of natural numbers induced when A245704 is restricted to {1} and binary codes for polynomials reducible over GF(2): a(1) = 1, a(n) = A062298(A245704(A091242(n-1))).

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