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 1-5 of 5 results.

A243501 Permutation of even numbers: a(n) = 2*A048673(n).

Original entry on oeis.org

2, 4, 6, 10, 8, 16, 12, 28, 26, 22, 14, 46, 18, 34, 36, 82, 20, 76, 24, 64, 56, 40, 30, 136, 50, 52, 126, 100, 32, 106, 38, 244, 66, 58, 78, 226, 42, 70, 86, 190, 44, 166, 48, 118, 176, 88, 54, 406, 122, 148, 96, 154, 60, 376, 92, 298, 116, 94, 62, 316, 68, 112, 276, 730, 120
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2014

Keywords

Links

Crossrefs

Cf. A243502, A245447, A245448, A244319, A245605-A245606, A245607-A245608.

Formula

a(n) = 2*A048673(n).
a(n) = A003961(n) + 1.
a(n) = A243502(A245447(n)).

A245448 Permutation of natural numbers: a(n) = A064216(A064216(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 11, 10, 7, 9, 14, 17, 31, 13, 6, 12, 34, 8, 23, 59, 41, 71, 16, 19, 39, 25, 26, 58, 37, 61, 30, 44, 22, 33, 49, 18, 85, 86, 15, 38, 69, 29, 151, 35, 55, 42, 107, 57, 97, 106, 21, 191, 122, 53, 111, 134, 74, 145, 109, 46, 82, 89, 50, 47, 36, 157, 133, 121, 43, 92, 110, 68, 52, 131, 28
Offset: 1

Views

Author

Antti Karttunen, Jul 22 2014

Keywords

Links

Crossrefs

Inverse: A245447.
Fixed points: A245449.
Cf. A064216, A243501, A243502.

Programs

Formula

a(n) = A064216(A064216(n)).
For all n >= 1, A243502(n) = A243501(a(n)).

A249734 Even bisection of A003961: Replace in 2n each prime factor p(k) with prime p(k+1).

Original entry on oeis.org

3, 9, 15, 27, 21, 45, 33, 81, 75, 63, 39, 135, 51, 99, 105, 243, 57, 225, 69, 189, 165, 117, 87, 405, 147, 153, 375, 297, 93, 315, 111, 729, 195, 171, 231, 675, 123, 207, 255, 567, 129, 495, 141, 351, 525, 261, 159, 1215, 363, 441, 285, 459, 177, 1125, 273, 891, 345, 279, 183, 945, 201, 333, 825, 2187, 357, 585, 213, 513, 435, 693, 219, 2025, 237, 369
Offset: 1

Views

Author

Antti Karttunen, Nov 23 2014

Keywords

Links

Crossrefs

Row 2 of A246278.
Cf. A249735 (the other bisection of A003961).
Cf. A016945, A048673, A064216, A064989, A249827, A243501, A243502.
Cf. also A000079, A000244.

Formula

a(n) = A003961(2*n).
a(n) = 3 * A003961(n).
a(n) = A064989(A249827(n)).
a(n) = A003961(A243501(A064216(n))).
a(n) = A003961(A243502(A048673(n))).
a(n) = A016945(A048673(n)-1). [Permutation of A016945, 6n+3.]
Other identities. For all n >= 1:
a(A000079(n-1)) = A000244(n). [Maps each 2^n to 3^(n+1).]

A245447 Permutation of natural numbers: a(n) = A048673(A048673(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 14, 8, 17, 9, 7, 6, 15, 13, 10, 38, 22, 11, 35, 23, 122, 50, 32, 18, 86, 25, 26, 138, 74, 41, 30, 12, 101, 33, 16, 43, 64, 28, 39, 24, 81, 20, 45, 68, 31, 176, 59, 63, 171, 34, 62, 203, 72, 53, 239, 44, 76, 47, 27, 19, 125, 29, 149, 218, 277, 158, 182, 113, 71, 40
Offset: 1

Views

Author

Antti Karttunen, Jul 22 2014

Keywords

Links

Crossrefs

Inverse: A245448.
Fixed points: A245449.
Cf. A048673, A243501, A243502.

Programs

Formula

a(n) = A048673(A048673(n)).
a(n) = (1/2) * (1 + A003961((1/2) * (1+A003961(n)))). [Where A003961(n) shifts the prime factorization of n one step left.]
a(n) = ((A003961(A243501(n)/2)) + 1) / 2 = ((A003961(A243501(n))/3) + 1) / 2.
For all n >= 1, A243501(n) = A243502(a(n)).

A243500 Self-inverse permutation of natural numbers: a(2n) = A003961(A048673(n)), a(2n-1) = 2 * A245448(n).

Original entry on oeis.org

2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 22, 27, 20, 15, 14, 33, 18, 17, 28, 13, 34, 11, 62, 29, 26, 25, 12, 19, 24, 75, 68, 43, 16, 21, 46, 69, 118, 45, 82, 243, 142, 99, 32, 63, 38, 35, 78, 171, 50, 49, 52, 51, 116, 275, 74, 147, 122, 81, 60, 59, 88, 23, 44, 201, 66, 65, 98, 31, 36
Offset: 1

Views

Author

Antti Karttunen, Jul 18 2014

Keywords

Links

Crossrefs

Cf. A003961, A048673, A064989, A243502, A244319, A245448.

Formula

a(2n) = A003961(A048673(n)), a(2n-1) = 2 * A245448(n).
a(2n) = A003961(A048673(n)), a(2n-1) = A243502(A064989(2n-1)).
a(2n) = A003961((A003961(n)+1)/2), a(2n-1) = 2 * A064216(A064989(2n-1)).
Showing 1-5 of 5 results.

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