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.

Previous Showing 11-17 of 17 results.

A245608 Permutation of natural numbers, the even bisection of A245606 halved: a(n) = A245606(2*n)/2.

Original entry on oeis.org

1, 2, 3, 5, 4, 8, 13, 11, 6, 14, 18, 41, 7, 26, 28, 20, 9, 23, 63, 50, 25, 113, 313, 65, 12, 17, 88, 77, 172, 149, 43, 95, 16, 38, 33, 44, 10, 413, 163, 221, 19, 74, 48, 191, 22, 476, 118, 179, 49, 68, 138, 29, 39, 527, 78, 215, 31, 635, 1593, 227, 102, 71, 688, 242, 24, 122, 193, 104, 15, 98, 58, 176, 30, 32, 123
Offset: 1

Views

Author

Antti Karttunen, Jul 29 2014

Keywords

Links

Crossrefs

Inverse: A245607.
Cf. A003961, A048673, A245606, A245609-A245610, A245706, A245708, A245709, A245612, A244154, A243065-A243066.

Programs

Formula

a(n) = A245606(2*n)/2.
As a composition of related permutations:
a(n) = A048673(A245606(n)).
a(n) = A245708(A245706(n)).
Other identities:
For all n >= 0, a(2^n) = A245708(2^n). Moreover, A245709 gives all such k that a(k) = A245708(k).

A244982 Permutation of natural numbers: a(n) = A243285(A122111(2*n)).

Original entry on oeis.org

1, 2, 4, 3, 8, 6, 18, 5, 11, 14, 38, 10, 79, 30, 22, 7, 164, 15, 337, 20, 47, 64, 694, 16, 35, 134, 26, 43, 1419, 32, 2888, 9, 100, 279, 73, 24, 5850, 575, 208, 34, 11822, 67, 23836, 92, 56, 1177, 47975, 19, 112, 50, 428, 193, 96431, 42, 152, 71, 877, 2395, 193614, 52
Offset: 1

Views

Author

Antti Karttunen, Jul 20 2014

Keywords

Links

Crossrefs

Inverse: A244981.
Cf. A122111, A243285, A244983-A244984, A243505-A243506, A243065-A243066.

Programs

Formula

a(n) = A243285(A122111(2*n)).

A244984 Permutation of natural numbers: a(n) = A243283(A122111((2*n)-1)).

Original entry on oeis.org

1, 2, 3, 5, 4, 9, 14, 6, 23, 37, 10, 58, 8, 7, 90, 143, 15, 13, 225, 24, 355, 563, 12, 894, 17, 38, 1426, 20, 60, 2277, 3643, 19, 31, 5839, 96, 9398, 15155, 16, 27, 24518, 11, 39758, 50, 153, 64607, 42, 242, 80, 105250, 30, 171874, 281237, 26
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2014

Keywords

Links

Crossrefs

Inverse: A244983.
Cf. A122111, A243283, A244981-A244982, A243505-A243506, A243065-A243066, A006254, A244986.

Programs

Formula

a(n) = A243283(A122111((2*n)-1)).
a(n) = A243283(A105560((2*n)-1) * A243505(n)).
For all n >= 1, a(A006254(n)) = A244986(n+1).

A243062 Permutation of natural numbers, a composition of A048673 and A241909: a(n) = A241909(A048673(n)).

Original entry on oeis.org

1, 2, 4, 8, 3, 5, 9, 81, 64, 32, 16, 512, 6, 128, 15, 8192, 27, 6561, 25, 11, 625, 125, 18, 78125, 12, 729, 250, 45, 7, 65536, 256, 387420489, 162, 1024, 486, 1073741824, 54, 36, 16384, 2916, 243, 8388608, 49, 131072, 16807, 3125, 10, 17496, 262144, 531441, 121, 72, 75
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2014

Keywords

Comments

This is A241909-conjugate of A243066. Please see the comments at the latter sequence.

Links

Crossrefs

Inverse permutation: A243061.
Cf. A048673, A241909, A243065-A243066.

Programs

Formula

a(n) = A241909(A048673(n)).
a(n) = A241909(A243066(A241909(n))).

A244981 Permutation of natural numbers: a(n) = A122111(A102750(n)) / 2.

Original entry on oeis.org

1, 2, 4, 3, 8, 6, 16, 5, 32, 12, 9, 64, 128, 10, 18, 24, 256, 7, 48, 20, 512, 15, 1024, 36, 96, 27, 2048, 192, 72, 14, 4096, 30, 8192, 40, 25, 384, 16384, 11, 144, 80, 32768, 54, 28, 288, 768, 65536, 21, 131072, 1536, 50, 108, 60, 262144, 160, 576, 45, 524288, 1048576, 3072, 320, 81, 120, 2097152, 22, 6144, 4194304, 42
Offset: 1

Views

Author

Antti Karttunen, Jul 20 2014

Keywords

Links

Crossrefs

Inverse: A244982.
Cf. A122111, A102750, A244983-A244984, A243505-A243506, A243065-A243066.

Programs

Formula

a(n) = A122111(A102750(n)) / 2.

A244983 Permutation of natural numbers: a(1) = 1, a(n) = (1 + A122111(A070003(n-1))) / 2.

Original entry on oeis.org

1, 2, 3, 5, 4, 8, 14, 13, 6, 11, 41, 23, 18, 7, 17, 38, 25, 68, 32, 28, 122, 63, 9, 20, 113, 53, 39, 365, 95, 50, 33, 74, 203, 61, 188, 88, 10, 26, 1094, 158, 83, 46, 608, 313, 3281, 338, 123, 149, 59, 43, 221, 116, 284, 72, 263, 138, 1013, 12, 9842, 29, 1823, 248, 98, 563, 172, 60
Offset: 1

Views

Author

Antti Karttunen, Jul 21 2014

Keywords

Links

Crossrefs

Inverse: A244984.
Cf. A070003, A006254, A244986.
Related or similar permutations: A122111, A244981-A244982, A243505-A243506, A243065-A243066.

Programs

Formula

a(1) = 1, a(n) = (1 + A122111(A070003(n-1))) / 2.
For all n >= 1, a(A244986(n+1)) = A006254(n).

A243061 Permutation of natural numbers, a composition of A241909 and A064216: a(n) = A064216(A241909(n)).

Original entry on oeis.org

1, 2, 5, 3, 6, 13, 29, 4, 7, 47, 20, 25, 113, 95, 15, 11, 78, 23, 355, 158, 103, 267, 406, 89, 19, 1247, 17, 1237, 1577, 139, 660, 10, 221, 4363, 67, 38, 8179, 13109, 967, 393, 9266, 515, 21605, 4162, 28, 23601, 19578, 239, 43, 83, 987, 31247
Offset: 1

Views

Author

Antti Karttunen, Jun 02 2014

Keywords

Comments

This is A241909-conjugate of A243065. Please see the comments at the latter sequence.

Links

Crossrefs

Inverse permutation: A243062.
Cf. A064216, A241909, A243065-A243066.

Programs

  • PARI
    A064216(n) = A064989(n+n-1);
A064989(n) = { my(f = factor(n)); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f) };
A241909(n) = if(1==n||isprime(n),2^primepi(n),my(f=factor(n),h=1,i,m=1,p=1,k=1); while(k<=#f~, p = nextprime(1+p); i = primepi(f[k,1]); m *= p^(i-h); h = i; if(f[k,2]>1, f[k,2]--, k++)); (p*m));
A243061(n) = A064216(A241909(n)); \\ Antti Karttunen, Dec 10 2021
  • Scheme
    (define (A243061 n) (A064216 (A241909 n)))

Formula

a(n) = A064216(A241909(n)).
a(n) = A241909(A243065(A241909(n))).
Previous Showing 11-17 of 17 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.