cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A244990 After 1, numbers whose greatest prime factor is a prime with an even index; n such that A061395(n) is even.

Original entry on oeis.org

1, 3, 6, 7, 9, 12, 13, 14, 18, 19, 21, 24, 26, 27, 28, 29, 35, 36, 37, 38, 39, 42, 43, 48, 49, 52, 53, 54, 56, 57, 58, 61, 63, 65, 70, 71, 72, 74, 76, 78, 79, 81, 84, 86, 87, 89, 91, 95, 96, 98, 101, 104, 105, 106, 107, 108, 111, 112, 113, 114, 116, 117, 122, 126, 129, 130, 131, 133, 139, 140, 142, 143, 144
Offset: 1

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Author

Antti Karttunen, Jul 21 2014

Keywords

Comments

Equally, after 1, natural numbers n such that A006530(n) is in A031215.
A122111 maps each one of these numbers to a unique term of A028260 and vice versa.

Links

Crossrefs

Complement: A244991.
Cf. A006530, A028260, A031215, A061395, A122111, A244988, A244321, A244322.

Formula

For all n, A244988(a(n)) = n.

A244321 Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = 2*a(k), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = 1+(2*a(k)).

Original entry on oeis.org

1, 2, 3, 4, 6, 5, 7, 8, 9, 12, 10, 13, 11, 15, 14, 16, 18, 17, 19, 24, 25, 20, 26, 21, 22, 27, 23, 31, 29, 30, 28, 32, 36, 34, 33, 37, 35, 39, 49, 38, 48, 51, 41, 50, 40, 52, 42, 53, 43, 44, 54, 45, 55, 47, 46, 63, 59, 61, 62, 58, 57, 60, 65, 56, 73, 64, 72, 68, 66, 69
Offset: 1

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Author

Antti Karttunen, Jul 22 2014

Keywords

Links

Crossrefs

Inverse: A244322.
Cf. A244988, A244989, A244990, A244991, A244992.
Similar entanglement permutations: A135141, A237427, A243287, A243343, A243345.

Formula

a(1) = 1, and for n > 1, if A244992(n) = 1 [i.e. the greatest prime factor of n has an odd index], a(n) = 2 * A244321(A244989(n)), otherwise, a(n) = 1 + (2 * A244321(A244988(n)-1)).
For all n >= 1, A000035(a(n)) = 1 - A244992(n).

A244989 Partial sums of A244992: a(1) = 0, and for n >= 1, a(n) = A244992(n) + a(n-1); Inverse function for A244991.

Original entry on oeis.org

0, 1, 1, 2, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 8, 9, 9, 9, 10, 10, 11, 12, 12, 13, 13, 13, 13, 13, 14, 15, 16, 17, 18, 18, 18, 18, 18, 18, 19, 20, 20, 20, 21, 22, 23, 24, 24, 24, 25, 26, 26, 26, 26, 27, 27, 27, 27, 28, 29, 29, 30, 30, 31, 31, 32, 33, 34, 35, 35, 35, 35, 36, 36, 37
Offset: 1

Views

Author

Antti Karttunen, Jul 22 2014

Keywords

Links

Crossrefs

Cf. A244988, A244991, A244992, A244321.

Formula

a(1) = 0, and for n >= 1, a(n) = A244992(n) + a(n-1).
a(n) = n - A244988(n).
For all n >= 1, a(A244991(n)) = n. [This works as an inverse function for the injection A244991].

A245614 Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = A026424(a(k)), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = A028260(1+a(k)).

Original entry on oeis.org

1, 2, 4, 3, 7, 6, 10, 5, 9, 12, 11, 16, 15, 24, 18, 8, 17, 14, 22, 20, 26, 19, 29, 25, 28, 36, 35, 55, 39, 44, 31, 13, 30, 27, 21, 38, 34, 51, 46, 42, 37, 57, 40, 47, 32, 52, 45, 62, 56, 50, 68, 60, 82, 81, 67, 121, 86, 93, 105, 72, 65, 79, 33, 59, 64, 23, 53, 48, 41, 58, 49, 85, 71, 77, 66, 111, 99
Offset: 1

Views

Author

Antti Karttunen, Jul 27 2014

Keywords

Comments

This shares with the permutation A122111 the property that each term of A244990 is mapped to a unique term of A028260 and each term of A244991 is mapped to a unique term of A026424.

Links

Crossrefs

Inverse: A245613.
Cf. A026424, A028260, A066829, A244988, A244989, A244990, A244991, A244992, A122111.
Similar permutations: A244321, A244322, A245604, A227413, A237126, A243288, A243344, A243346, A245606.

Formula

a(1) = 1, and for n > 1, if A244992(n) = 1, a(n) = A026424(a(A244989(n))), otherwise a(n) = A028260(1+a(A244988(n)-1)).
As a composition of related permutations:
a(n) = A245604(A244321(n)).
For all n >= 1, A244992(n) = A066829(a(n)).
Showing 1-4 of 4 results.

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