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.

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A264989 Self-inverse permutation of nonnegative integers: a(n) = (A264987(n)-1) / 2.

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 6, 7, 11, 14, 16, 8, 17, 13, 9, 18, 10, 12, 15, 19, 20, 47, 22, 29, 56, 34, 38, 41, 43, 23, 50, 49, 32, 59, 25, 35, 44, 52, 26, 53, 40, 27, 54, 28, 36, 45, 55, 21, 48, 31, 30, 57, 37, 39, 42, 46, 24, 51, 58, 33, 60, 61, 101, 128, 142, 74, 155, 67, 83, 164, 88, 110, 137, 169, 65, 146, 103, 92, 173, 115, 119, 122
Offset: 0

Views

Author

Antti Karttunen, Dec 05 2015

Keywords

Links

Crossrefs

Cf. A016825, A263272, A263273, A264987, A264991, A264992.
Cf. also A264985.

Formula

a(n) = (A264987(n)-1) / 2.
a(n) = (1/2) * (A263272((2*n)+1) - 1).
a(n) = (1/4) * (A263273(4n + 2) - 2).

A264978 Self-inverse permutation of nonnegative integers: a(n) = A263273(8*n)/8.

Original entry on oeis.org

0, 1, 2, 3, 8, 5, 6, 7, 4, 9, 10, 17, 24, 26, 14, 15, 23, 11, 18, 29, 20, 21, 25, 16, 12, 22, 13, 27, 28, 19, 30, 71, 44, 51, 62, 35, 72, 89, 53, 78, 80, 41, 42, 68, 32, 45, 86, 59, 69, 77, 50, 33, 65, 38, 54, 83, 56, 87, 74, 47, 60, 61, 34, 63, 88, 52, 75, 79, 43, 48, 70, 31, 36, 85, 58, 66, 76, 49, 39, 67, 40, 81
Offset: 0

Views

Author

Antti Karttunen, Dec 06 2015

Keywords

Comments

Note that n=13 is the first point where this involution does not preserve the parity as a(13) = 26.

Links

Crossrefs

Cf. A263273, A263272, A264974.

Formula

a(n) = A263273(8*n)/8.
a(n) = A263272(4*n)/4.
a(n) = A264974(2*n)/2.
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

A266641 Permutation of nonnegative integers: a(n) = A264965(2*n) / 2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 11, 8, 9, 10, 13, 12, 7, 14, 15, 32, 23, 18, 35, 20, 33, 26, 19, 24, 29, 38, 27, 28, 17, 30, 37, 16, 21, 34, 113, 36, 41, 50, 87, 40, 31, 42, 77, 104, 45, 110, 101, 96, 25, 22, 69, 68, 95, 54, 47, 56, 39, 86, 83, 60, 59, 74, 99, 92, 65, 114, 97, 44, 81, 70, 49, 72, 89, 82, 75, 88, 73, 66, 121, 80, 51
Offset: 0

Views

Author

Antti Karttunen, Jan 04 2016

Keywords

Links

Crossrefs

Inverse: A266642.
Cf. A057889, A263272, A264965, A265329, A265369, A266635, A266636, A266643, A266644.

Formula

a(n) = A264965(2*n) / 2.
As a composition of related permutations:
a(n) = A263272(A057889(n)).

A266642 Permutation of nonnegative integers: a(n) = A264966(2*n) / 2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 13, 8, 9, 10, 7, 12, 11, 14, 15, 32, 29, 18, 23, 20, 33, 50, 17, 24, 49, 22, 27, 28, 25, 30, 41, 16, 21, 34, 19, 36, 31, 26, 57, 40, 37, 42, 125, 68, 45, 106, 55, 96, 71, 38, 81, 88, 89, 54, 101, 56, 117, 118, 61, 60, 83, 82, 99, 116, 65, 78, 119, 52, 51, 70, 113, 72, 77, 62, 75, 92, 43, 114, 107, 80, 69
Offset: 0

Views

Author

Antti Karttunen, Jan 04 2016

Keywords

Links

Crossrefs

Inverse: A266641.
Cf. A057889, A263272, A264966, A265329, A265369, A266635, A266636, A266643, A266644.

Programs

Formula

a(n) = A264966(2*n) / 2.
As a composition of related permutations:
a(n) = A057889(A263272(n)).

A264984 Even bisection of A263273; terms of A263262 doubled.

Original entry on oeis.org

0, 2, 4, 6, 8, 10, 12, 22, 16, 18, 20, 14, 24, 26, 28, 30, 64, 46, 36, 58, 40, 66, 76, 34, 48, 70, 52, 54, 56, 38, 60, 74, 32, 42, 68, 50, 72, 62, 44, 78, 80, 82, 84, 190, 136, 90, 172, 118, 192, 226, 100, 138, 208, 154, 108, 166, 112, 174, 220, 94, 120, 202, 148, 198, 184, 130
Offset: 0

Views

Author

Antti Karttunen, Dec 05 2015

Keywords

Crossrefs

Cf. A000035, A010673, A010873, A263272, A263273, A264983, A264975.

Programs

  • Python
    from sympy import factorint
from sympy.ntheory.factor_ import digits
from operator import mul
def a030102(n): return 0 if n==0 else int(''.join(map(str, digits(n, 3)[1:][::-1])), 3)
def a038502(n):
    f=factorint(n)
    return 1 if n==1 else reduce(mul, [1 if i==3 else i**f[i] for i in f])
def a038500(n): return n/a038502(n)
def a263273(n): return 0 if n==0 else a030102(a038502(n))*a038500(n)
def a(n): return a263273(2*n) # Indranil Ghosh, May 22 2017
  • Scheme
    (define (A264984 n) (A263273 (+ n n)))

Formula

a(n) = 2 * A263272(n).
a(n) = A263273(2*n).
Other identities. For all n >= 0:
A010873(a(n)) = 2 * A000035(n) = A010673(n).

A265342 Permutation of even numbers: a(n) = 2 * A265351(n).

Original entry on oeis.org

0, 2, 4, 6, 8, 22, 12, 10, 16, 18, 20, 58, 24, 26, 76, 66, 64, 70, 36, 14, 40, 30, 28, 34, 48, 46, 52, 54, 56, 166, 60, 62, 184, 174, 172, 178, 72, 74, 220, 78, 80, 238, 228, 226, 232, 198, 68, 202, 192, 190, 196, 210, 208, 214, 108, 38, 112, 42, 44, 130, 120, 118, 124, 90, 32, 94, 84, 82, 88, 102, 100, 106, 144
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Iterating this sequence as 1, a(1), a(a(1)), a(a(a(1))), ... yields A264980.

Links

Crossrefs

Cf. A265351.
Cf. also A265341, A263273, A264980.

Programs

  • Python
    from sympy import factorint
from sympy.ntheory.factor_ import digits
from operator import mul
def a030102(n): return 0 if n==0 else int(''.join(map(str, digits(n, 3)[1:][::-1])), 3)
def a038502(n):
    f=factorint(n)
    return 1 if n==1 else reduce(mul, [1 if i==3 else i**f[i] for i in f])
def a038500(n): return n/a038502(n)
def a263273(n): return 0 if n==0 else a030102(a038502(n))*a038500(n)
def a263272(n): return a263273(2*n)/2
def a(n): return 2*a263272(a263273(n)) # Indranil Ghosh, May 25 2017
  • Scheme
    (define (A265342 n) (* 2 (A265351 n)))

Formula

a(n) = 2 * A265351(n).

A265361 Permutation of nonnegative integers: a(n) = A264974(A264989(n)).

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 6, 7, 19, 14, 8, 16, 17, 13, 9, 18, 10, 12, 15, 11, 20, 59, 34, 55, 56, 22, 58, 41, 23, 43, 44, 35, 46, 47, 25, 49, 50, 26, 52, 53, 40, 27, 54, 28, 36, 45, 29, 21, 24, 37, 30, 33, 31, 39, 42, 32, 48, 51, 38, 57, 60, 61, 181, 176, 62, 178, 179, 115, 163, 164, 64, 166, 167, 65, 169, 170, 103, 172, 173, 67, 175, 122
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of permutations obtained from the bisections of A263272.

Links

Crossrefs

Inverse: A265362.
Cf. A263272, A264974, A264989.

Programs

A265362 Permutation of nonnegative integers: a(n) = A264989(A264974(n)).

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 6, 7, 10, 14, 16, 19, 17, 13, 9, 18, 11, 12, 15, 8, 20, 47, 25, 28, 48, 34, 37, 41, 43, 46, 50, 52, 55, 51, 22, 31, 44, 49, 58, 53, 40, 27, 54, 29, 30, 45, 32, 33, 56, 35, 36, 57, 38, 39, 42, 23, 24, 59, 26, 21, 60, 61, 64, 128, 70, 73, 143, 79, 82, 144, 88, 91, 129, 97, 100, 146, 106, 109, 147, 115, 118, 122
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of permutations obtained from the bisections of A263272.

Links

Crossrefs

Inverse: A265361.
Cf. A263272, A264974, A264989.

Programs

Formula

a(n) = A264989(A264974(n)).
Previous Showing 21-28 of 28 results.

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