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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A065278 A065276 conjugated with A059893, inverse of A065277.

Original entry on oeis.org

2, 4, 1, 8, 3, 10, 6, 16, 5, 18, 7, 20, 12, 22, 14, 32, 9, 34, 11, 36, 13, 38, 15, 40, 24, 42, 26, 44, 28, 46, 30, 64, 17, 66, 19, 68, 21, 70, 23, 72, 25, 74, 27, 76, 29, 78, 31, 80, 48, 82, 50, 84, 52, 86, 54, 88, 56, 90, 58, 92, 60, 94, 62, 128, 33, 130, 35, 132, 37, 134, 39
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Comments

This permutation of N induces also such permutation of Z, that p(i)-i >= 0 for all i.

Links

Crossrefs

The associated siteswap sequence is A065279.

Formula

a(n) = A059893(A065276(A059893(n)))

A065284 A065282 conjugated with A059893, inverse of A065283.

Original entry on oeis.org

1, 6, 2, 12, 4, 14, 3, 24, 8, 26, 10, 28, 5, 30, 7, 48, 16, 50, 18, 52, 20, 54, 22, 56, 9, 58, 11, 60, 13, 62, 15, 96, 32, 98, 34, 100, 36, 102, 38, 104, 40, 106, 42, 108, 44, 110, 46, 112, 17, 114, 19, 116, 21, 118, 23, 120, 25, 122, 27, 124, 29, 126, 31, 192, 64, 194, 66
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Comments

This permutation of N induces also such permutation of Z, that p(i)-i >= 0 for all i.

Links

Crossrefs

The associated siteswap sequence is A065285.

Formula

a(n) = A059893(A065282(A059893(n)))

A065290 A065288 conjugated with A059893, inverse of A065289.

Original entry on oeis.org

2, 4, 1, 8, 6, 10, 3, 16, 12, 18, 14, 20, 5, 22, 7, 32, 24, 34, 26, 36, 28, 38, 30, 40, 9, 42, 11, 44, 13, 46, 15, 64, 48, 66, 50, 68, 52, 70, 54, 72, 56, 74, 58, 76, 60, 78, 62, 80, 17, 82, 19, 84, 21, 86, 23, 88, 25, 90, 27, 92, 29, 94, 31, 128, 96, 130, 98, 132, 100, 134
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Comments

This permutation of N induces also such permutation of Z, that p(i)-i >= 0 for all i.

Links

Crossrefs

The associated siteswap sequence is A065291.

Formula

a(n) = A059893(A065288(A059893(n)))

A065259 A057114 conjugated with A059893, inverse of A065260.

Original entry on oeis.org

3, 1, 7, 2, 11, 5, 15, 4, 19, 9, 23, 6, 27, 13, 31, 8, 35, 17, 39, 10, 43, 21, 47, 12, 51, 25, 55, 14, 59, 29, 63, 16, 67, 33, 71, 18, 75, 37, 79, 20, 83, 41, 87, 22, 91, 45, 95, 24, 99, 49, 103, 26, 107, 53, 111, 28, 115, 57, 119, 30, 123, 61, 127, 32, 131, 65, 135, 34, 139
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Examples

			G.f. = 3*x + x^2 + 7*x^3 + 2*x^4 + 11*x^5 + 5*x^6 + 15*x^7 + 4*x^8 + ...

Links

Programs

  • PARI
    Vec(x*(3+x+7*x^2+2*x^3+5*x^4+3*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)^2) + O(x^100)) \\ Colin Barker, Oct 29 2016
  • PARI
    {a(n) = if( n%2, 2*n+1, n%4, n-1, n/2)}; /* Michael Somos, Nov 06 2016 */

Formula

a(n) = A059893(A057114(A059893(n))).
a(2*k+1) = 4*k+3, a(4*k+2) = 4*k+1, a(4*k+4) = 2*k+2. - Ralf Stephan, Jun 10 2005
a(n) = (11*n+2-(5*n+6)*(-1)^n+(n-2)*(1+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/8. - Luce ETIENNE, Oct 29 2016
From Colin Barker, Oct 29 2016: (Start)
a(n) = 2*a(n-4) - a(n-8) for n>8.
G.f.: x*(3 + x + 7*x^2 + 2*x^3 + 5*x^4 + 3*x^5 + x^6)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2). (End)

A153153 Permutation of natural numbers: A059893-conjugate of A003188.

Original entry on oeis.org

0, 1, 3, 2, 5, 6, 7, 4, 9, 10, 15, 12, 13, 14, 11, 8, 17, 18, 23, 20, 29, 30, 27, 24, 25, 26, 31, 28, 21, 22, 19, 16, 33, 34, 39, 36, 45, 46, 43, 40, 57, 58, 63, 60, 53, 54, 51, 48, 49, 50, 55, 52, 61, 62, 59, 56, 41, 42, 47, 44, 37, 38, 35, 32, 65, 66, 71, 68, 77, 78, 75, 72
Offset: 0

Views

Author

Antti Karttunen, Dec 20 2008

Keywords

Links

Crossrefs

Inverse: A153154. a(n) = A059893(A003188(A059893(n))).

Programs

  • R
    a <- 1
maxlevel <- 5 # by choice
#
for(m in 0:maxlevel) for(k in 0:(2^m-1)){
  a[2^(m+1)+2*k  ] <- 2*a[2^(m+1)-1-k] + 1
  a[2^(m+1)+2*k+1] <- 2*a[2^m+k]
}
a <- c(0,a)
# Yosu Yurramendi, Jan 25 2020

Formula

a(n) = A065190(A231550(n)). - Yosu Yurramendi, Jan 15 2020
a(1) = 1, a(2^(m+1)+2*k) = 2*a(2^(m+1)-1-k), a(2^(m+1)+2*k+1) = 2*a(2^m+k), m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Jan 25 2020

A154438 Permutation of nonnegative integers: A059893-conjugate of A154436.

Original entry on oeis.org

0, 1, 3, 2, 7, 4, 5, 6, 15, 12, 9, 10, 11, 8, 13, 14, 31, 28, 25, 26, 19, 16, 21, 22, 23, 20, 17, 18, 27, 24, 29, 30, 63, 60, 57, 58, 51, 48, 53, 54, 39, 36, 33, 34, 43, 40, 45, 46, 47, 44, 41, 42, 35, 32, 37, 38, 55, 52, 49, 50, 59, 56, 61, 62, 127, 124, 121, 122, 115, 112
Offset: 0

Views

Author

Antti Karttunen, Jan 17 2009

Keywords

Comments

This permutation is induced by the same Lamplighter group generating wreath recursion (binary transducer) as A154436, starting from the active (swapping) state a, but in contrast to it, this one rewrites the bits from the least significant end up to the second most significant bit.

Links

Crossrefs

Inverse: A154437.
a(n) = A059893(A154436(A059893(n))) = A054429(A153153(A054429(n))).

Programs

  • R
    maxlevel <- 5 # by choice
a <- 1
for(m in 0:maxlevel) for(k in 0:(2^m-1)){
  a[2^(m+2)-1-2*k] <- 2*a[2^m+k]
  a[2^(m+1)  +2*k] <- 2*a[2^m+k] + 1
}
(a <- c(0,a))
# Yosu Yurramendi, Apr 10 2020

Formula

a(0) = 0, a(1) = 1, m > 0, 0 <= k < 2^m a(2^(m+2)-1-2*k) = 2*a(2^m+k),
a(2^(m+1)+2*k) = 2*a(2^m+k) + 1. - Yosu Yurramendi, Apr 10 2020

A065265 A065263 conjugated with A059893, inverse of A065266.

Original entry on oeis.org

3, 1, 7, 2, 13, 5, 15, 4, 25, 6, 27, 11, 29, 9, 31, 8, 49, 10, 51, 12, 53, 14, 55, 23, 57, 21, 59, 19, 61, 17, 63, 16, 97, 18, 99, 20, 101, 22, 103, 24, 105, 26, 107, 28, 109, 30, 111, 47, 113, 45, 115, 43, 117, 41, 119, 39, 121, 37, 123, 35, 125, 33, 127, 32, 193, 34, 195
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Links

Formula

a(n) = A059893(A065263(A059893(n)))

A065271 A065269 conjugated with A059893, inverse of A065272.

Original entry on oeis.org

1, 3, 5, 7, 9, 2, 11, 15, 17, 13, 19, 4, 21, 6, 23, 31, 33, 29, 35, 27, 37, 25, 39, 8, 41, 10, 43, 12, 45, 14, 47, 63, 65, 61, 67, 59, 69, 57, 71, 55, 73, 53, 75, 51, 77, 49, 79, 16, 81, 18, 83, 20, 85, 22, 87, 24, 89, 26, 91, 28, 93, 30, 95, 127, 129, 125, 131, 123, 133, 121
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Links

Formula

a(n) = A059893(A065269(A059893(n)))

A065277 A065275 conjugated with A059893, inverse of A065278.

Original entry on oeis.org

3, 1, 5, 2, 9, 7, 11, 4, 17, 6, 19, 13, 21, 15, 23, 8, 33, 10, 35, 12, 37, 14, 39, 25, 41, 27, 43, 29, 45, 31, 47, 16, 65, 18, 67, 20, 69, 22, 71, 24, 73, 26, 75, 28, 77, 30, 79, 49, 81, 51, 83, 53, 85, 55, 87, 57, 89, 59, 91, 61, 93, 63, 95, 32, 129, 34, 131, 36, 133, 38, 135
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Links

Formula

a(n) = A059893(A065275(A059893(n)))

A065283 A065281 conjugated with A059893, inverse of A065284.

Original entry on oeis.org

1, 3, 7, 5, 13, 2, 15, 9, 25, 11, 27, 4, 29, 6, 31, 17, 49, 19, 51, 21, 53, 23, 55, 8, 57, 10, 59, 12, 61, 14, 63, 33, 97, 35, 99, 37, 101, 39, 103, 41, 105, 43, 107, 45, 109, 47, 111, 16, 113, 18, 115, 20, 117, 22, 119, 24, 121, 26, 123, 28, 125, 30, 127, 65, 193, 67, 195
Offset: 1

Views

Author

Antti Karttunen, Oct 28 2001

Keywords

Links

Formula

a(n) = A059893(A065281(A059893(n)))
Previous Showing 11-20 of 113 results. Next

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