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 1-10 of 10 results.

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).

A265352 Permutation of nonnegative integers: a(n) = A263273(A263272(n)).

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 6, 19, 8, 9, 10, 5, 12, 13, 22, 21, 64, 23, 18, 55, 20, 57, 58, 25, 24, 73, 26, 27, 28, 11, 30, 31, 16, 15, 46, 17, 36, 37, 14, 39, 40, 67, 66, 199, 68, 63, 190, 65, 192, 193, 70, 69, 208, 71, 54, 163, 56, 165, 166, 61, 60, 181, 62, 171, 172, 59, 174, 175, 76, 75, 226, 77, 72, 217, 74, 219, 220, 79, 78, 235, 80, 81
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of A263273 with the permutation obtained from its even bisection.

Links

Crossrefs

Inverse: A265351.
Cf. A263272, A263273, A264974, A265368.
Cf. also A265354, A265355, A265356

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(a263273(2*n)/2) # Indranil Ghosh, Jun 08 2017
  • Scheme
    (define (A265352 n) (A263273 (A263272 n)))

Formula

a(n) = A263273(A263272(n)).
As a composition of other related permutations:
a(n) = A265368(A264974(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

A265353 Permutation of nonnegative integers: a(n) = A264985(A263273(n)).

Original entry on oeis.org

0, 1, 3, 2, 4, 10, 6, 9, 12, 5, 7, 19, 8, 13, 31, 24, 28, 37, 15, 11, 33, 18, 27, 30, 21, 36, 39, 14, 16, 46, 23, 25, 73, 69, 55, 64, 17, 22, 58, 26, 40, 94, 78, 85, 112, 51, 34, 100, 72, 82, 91, 75, 109, 118, 42, 32, 96, 20, 35, 105, 60, 99, 102, 45, 29, 87, 54, 81, 84, 57, 90, 93, 48, 38, 114, 63, 108, 111, 66, 117, 120, 41
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of A263273 with the permutation obtained from its odd bisection.

Links

Crossrefs

Inverse: A265354.
Cf. A263273, A264985.
Cf. also A265341, A265351, A265355, A265356.

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 a264985(n): return (a263273(2*n + 1) - 1)/2
def a(n): return a264985(a263273(n)) # Indranil Ghosh, May 22 2017
  • Scheme
    (define (A265353 n) (A264985 (A263273 n)))

Formula

a(n) = A264985(A263273(n)).

A265355 Permutation of nonnegative integers: a(n) = A263272(A264985(n)).

Original entry on oeis.org

0, 1, 3, 2, 4, 9, 6, 10, 12, 5, 11, 7, 8, 13, 27, 18, 28, 36, 15, 29, 21, 24, 37, 30, 33, 31, 39, 14, 32, 16, 17, 38, 19, 20, 34, 22, 23, 35, 25, 26, 40, 81, 54, 82, 108, 45, 83, 63, 72, 109, 90, 99, 85, 117, 42, 86, 48, 51, 110, 57, 60, 88, 66, 69, 89, 75, 78, 118, 84, 87, 91, 93, 96, 92, 102, 105, 112, 111, 114, 94, 120, 41
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of permutations obtained from the bisections of A263273.

Links

Crossrefs

Inverse: A265356.
Cf. A263272, A263273, A264985.
Cf. also A265351, A265352, A265353, A265354, A265357, A265358.

Programs

Formula

a(n) = A263272(A264985(n)).

A265356 Permutation of nonnegative integers: a(n) = A264985(A263272(n)).

Original entry on oeis.org

0, 1, 3, 2, 4, 9, 6, 11, 12, 5, 7, 10, 8, 13, 27, 18, 29, 30, 15, 32, 33, 20, 35, 36, 21, 38, 39, 14, 16, 19, 23, 25, 28, 24, 34, 37, 17, 22, 31, 26, 40, 81, 54, 83, 84, 45, 86, 87, 56, 89, 90, 57, 92, 93, 42, 95, 96, 59, 98, 99, 60, 101, 102, 47, 104, 105, 62, 107, 108, 63, 110, 111, 48, 113, 114, 65, 116, 117, 66, 119, 120, 41
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of permutations obtained from the bisections of A263273.

Links

Crossrefs

Inverse: A265355.
Cf. A263272, A263273, A264985.
Cf. also A265351, A265352, A265353, A265354, A265357, A265358.

Programs

Formula

a(n) = A264985(A263272(n)).

A265904 Self-inverse permutation of nonnegative integers: a(n) = A263272(A263273(A263272(n))).

Original entry on oeis.org

0, 1, 2, 3, 4, 11, 6, 29, 8, 9, 10, 5, 12, 13, 38, 33, 92, 17, 18, 83, 20, 87, 110, 35, 24, 89, 26, 27, 28, 7, 30, 37, 32, 15, 86, 23, 36, 31, 14, 39, 40, 119, 114, 281, 44, 99, 254, 65, 276, 335, 98, 51, 260, 71, 54, 245, 56, 249, 326, 101, 60, 263, 74, 261, 272, 47, 330, 353, 116, 105, 278, 53, 72, 251, 62, 267, 332, 107, 78, 269, 80, 81, 82, 19
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2016

Keywords

Comments

A263273 conjugated with the permutation obtained from its even bisection.

Links

Crossrefs

Cf. A000035, A263272, A263273, A265351, A265352.
Cf. also A265902.
Cf. A265369, A266190, A266401, A266403 (other conjugates or similar derivations of A263273).

Programs

  • Mathematica
    f[n_] := Block[{g, h}, g[x_] := x/3^IntegerExponent[x, 3]; h[x_] := x/g@ x; If[n == 0, 0, FromDigits[Reverse@ IntegerDigits[#, 3], 3] &@g[n] h[n]]]; t = Table[f[2 n]/2, {n, 0, 1000}]; Table[t[[f[t[[n + 1]]] + 1]], {n, 0, 83}] (* Michael De Vlieger, Jan 04 2016, after Jean-François Alcover at A263273 *)
  • 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 a263272(a263273(a263272(n))) # Indranil Ghosh, May 25 2017
  • Scheme
    (define (A265904 n) (A263272 (A263273 (A263272 n))))

Formula

a(n) = A263272(A263273(A263272(n))).
As a composition of related permutations:
a(n) = A263272(A265352(n)).
a(n) = A265351(A263272(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]

A265357 Permutation of nonnegative integers: a(n) = A264989(A263272(n)).

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 6, 8, 11, 14, 16, 7, 17, 13, 9, 18, 32, 29, 15, 23, 20, 59, 26, 12, 56, 35, 38, 41, 43, 19, 50, 52, 10, 47, 25, 34, 44, 49, 22, 53, 40, 27, 54, 86, 83, 45, 95, 33, 167, 98, 30, 164, 89, 92, 42, 68, 24, 176, 71, 21, 60, 62, 65, 140, 77, 74, 179, 80, 36, 57, 113, 110, 137, 104, 101, 170, 107, 39, 173, 116, 119, 122
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of A263272 with the permutation obtained from its odd bisection.

Links

Crossrefs

Inverse: A265358.
Cf. A263272, A264989.
Cf. also A265351, A265352, A265353, A265354, A265355, A265356.

Programs

Formula

a(n) = A264989(A263272(n)).

A265358 Permutation of nonnegative integers: a(n) = A263272(A264989(n)).

Original entry on oeis.org

0, 1, 2, 5, 4, 3, 6, 11, 7, 14, 32, 8, 23, 13, 9, 18, 10, 12, 15, 29, 20, 59, 38, 19, 56, 34, 22, 41, 95, 17, 50, 113, 16, 47, 35, 25, 68, 104, 26, 77, 40, 27, 54, 28, 36, 45, 83, 33, 96, 37, 30, 87, 31, 39, 42, 86, 24, 69, 110, 21, 60, 101, 61, 176, 302, 62, 185, 119, 55, 164, 100, 58, 167, 299, 65, 194, 115, 64, 191, 103, 67, 122
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of A263272 with the permutation obtained from its odd bisection.

Links

Crossrefs

Inverse: A265357.
Cf. A263272, A264989.
Cf. also A265351, A265352, A265353, A265354, A265355, A265356.
Cf. A265361, A265362.

Programs

Formula

a(n) = A263272(A264989(n)).

A265367 Permutation of nonnegative integers: a(n) = A264974(A263272(A263273(n))).

Original entry on oeis.org

0, 1, 2, 3, 4, 19, 6, 5, 16, 9, 10, 55, 12, 13, 58, 57, 46, 49, 18, 7, 20, 15, 14, 17, 48, 43, 52, 27, 28, 163, 30, 37, 172, 165, 136, 145, 36, 31, 166, 39, 40, 175, 174, 139, 148, 171, 22, 181, 138, 127, 154, 147, 130, 157, 54, 11, 56, 21, 34, 169, 60, 47, 142, 45, 8, 59, 42, 41, 50, 51, 44, 53, 144, 25, 178, 129, 124, 151, 156, 133, 160, 81
Offset: 0

Views

Author

Antti Karttunen, Dec 07 2015

Keywords

Comments

Composition of A263273 with the permutations obtained from its bisection (A263272) and quadrisection (A264974), in that order from right to left.

Links

Crossrefs

Inverse: A265368.
Cf. A263272, A263273, A264974, A264975, A265351.

Programs

Formula

a(n) = A264974(A263272(A263273(n))).
As a composition of other related permutations:
a(n) = A264974(A265351(n)).
a(n) = A264975(A263273(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).

A265902 Self-inverse permutation of nonnegative integers: a(n) = A263273(A263272(A263273(n))).

Original entry on oeis.org

0, 1, 2, 3, 4, 19, 6, 7, 8, 9, 10, 55, 12, 13, 58, 57, 64, 73, 18, 5, 20, 21, 22, 25, 24, 23, 26, 27, 28, 163, 30, 37, 172, 165, 190, 217, 36, 31, 166, 39, 40, 175, 174, 193, 220, 171, 46, 181, 192, 199, 226, 219, 208, 235, 54, 11, 56, 15, 14, 59, 60, 65, 74, 63, 16, 61, 66, 67, 76, 75, 70
Offset: 0

Views

Author

Antti Karttunen, Jan 02 2016

Keywords

Links

Crossrefs

Cf. A000035, A263272, A263273, A265351, A265352.
Cf. also A265904, A266189.

Programs

Formula

a(n) = A263273(A263272(A263273(n))).
As a composition of related permutations:
a(n) = A263273(A265351(n)).
a(n) = A265352(A263273(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
Showing 1-10 of 10 results.

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