A265352 -id:A265352 - cp's OEIS frontend

A265351 Permutation of nonnegative integers: a(n) = A263272(A263273(n)).

0, 1, 2, 3, 4, 11, 6, 5, 8, 9, 10, 29, 12, 13, 38, 33, 32, 35, 18, 7, 20, 15, 14, 17, 24, 23, 26, 27, 28, 83, 30, 31, 92, 87, 86, 89, 36, 37, 110, 39, 40, 119, 114, 113, 116, 99, 34, 101, 96, 95, 98, 105, 104, 107, 54, 19, 56, 21, 22, 65, 60, 59, 62, 45, 16, 47, 42, 41, 44, 51, 50, 53, 72, 25, 74, 69, 68, 71, 78, 77, 80, 81

Offset: 0

Antti Karttunen, Dec 07 2015

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

Antti Karttunen, Table of n, a(n) for n = 0..9841
Index entries for sequences that are permutations of the natural numbers

Inverse: A265352.
Cf. A263272, A263273, A264974, A265367.
Cf. also A265342, A265353, A265355, A265356.

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(n)) # Indranil Ghosh, May 25 2017

(define (A265351 n) (A263272 (A263273 n)))

a(n) = A263272(A263273(n)).
As a composition of other related permutations:
a(n) = A264974(A265367(n)).
Other identities. For all n >= 0:
a(3*n) = 3*a(n).
a(n) = A265342(n)/2.

A265354 Permutation of nonnegative integers: a(n) = A263273(A264985(n)).

Original entry on oeis.org

0, 1, 3, 2, 4, 9, 6, 10, 12, 7, 5, 19, 8, 13, 27, 18, 28, 36, 21, 11, 57, 24, 37, 30, 15, 31, 39, 22, 16, 64, 23, 14, 55, 20, 46, 58, 25, 17, 73, 26, 40, 81, 54, 82, 108, 63, 29, 171, 72, 109, 90, 45, 85, 117, 66, 34, 192, 69, 38, 165, 60, 100, 174, 75, 35, 219, 78, 118, 84, 33, 91, 93, 48, 32, 138, 51, 112, 111, 42, 94, 120, 67

Offset: 0

Antti Karttunen, Dec 07 2015

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

Antti Karttunen, Table of n, a(n) for n = 0..9841
Index entries for sequences that are permutations of the natural numbers

Inverse: A265353.
Cf. A263273, A264985.
Cf. also A265352, A265355, A265356.

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 a263273(a264985(n)) # Indranil Ghosh, May 22 2017

(define (A265354 n) (A263273 (A264985 n)))

a(n) = A263273(A264985(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

Antti Karttunen, Dec 07 2015

Composition of permutations obtained from the bisections of A263273.

Antti Karttunen, Table of n, a(n) for n = 0..9841
Index entries for sequences that are permutations of the natural numbers

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

(define (A265355 n) (A263272 (A264985 n)))

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

Antti Karttunen, Dec 07 2015

Composition of permutations obtained from the bisections of A263273.

Antti Karttunen, Table of n, a(n) for n = 0..9841
Index entries for sequences that are permutations of the natural numbers

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

(define (A265356 n) (A264985 (A263272 n)))

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

A265331 One-based row index to A265345.

Original entry on oeis.org

1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 6, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 7, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 5, 1, 2, 1, 3, 1, 2, 1, 4, 1, 2, 1, 3, 1, 2, 1, 4

Offset: 1

Antti Karttunen, Dec 18 2015

Antti Karttunen, Table of n, a(n) for n = 1..19683

One more than A265330.
Cf. A007088, A007089, A263273, A265345, A265352.
Cf. A265911 (corresponding other index).
Differs from A001511 for the first time at n=32, where a(32) = 7, while A001511(32) = 6.

(definec (A265331 n) (if (odd? n) 1 (+ 1 (A265331 (A265352 (/ n 2))))))

a(n) = A001511(A263273(n)).

a(2n+1) = 1, a(2n) = 1 + a(A265352(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

Antti Karttunen, Jan 02 2016

A263273 conjugated with the permutation obtained from its even bisection.

Antti Karttunen, Table of n, a(n) for n = 0..6561
Index entries for sequences that are permutations of the natural numbers

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

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 *)

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

(define (A265904 n) (A263272 (A263273 (A263272 n))))

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.]

A265330 Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).

Original entry on oeis.org

0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3

Offset: 1

Antti Karttunen, Dec 18 2015

			For n = 32, in base-3 "1012" [= A007089(32)], when we reverse it, we get "2101" [= A007089(64)], and 2-adic valuation of 64 [= "1000000" = A007088(64)] is 6, thus a(32) = 6.

Antti Karttunen, Table of n, a(n) for n = 1..6561

One less than A265331.
Cf. A007088, A007089, A263273, A265345, A265352.
Cf. A265910 (corresponding other index).
Cf. also A265336, A265337, A265340.
Differs from A007814 for the first time at n=32, where a(32) = 6, while A007814(32) = 5.

a(n) = A007814(A263273(n)).

a(2n+1) = 0, a(2n) = 1 + a(A265352(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

Antti Karttunen, Dec 07 2015

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

Antti Karttunen, Table of n, a(n) for n = 0..9841
Index entries for sequences that are permutations of the natural numbers

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

(define (A265357 n) (A264989 (A263272 n)))

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

Antti Karttunen, Dec 07 2015

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

Antti Karttunen, Table of n, a(n) for n = 0..9841
Index entries for sequences that are permutations of the natural numbers

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

(define (A265358 n) (A263272 (A264989 n)))

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

A265910 Zero-based column index to array A265345.

Original entry on oeis.org

0, 0, 1, 0, 3, 1, 2, 0, 4, 2, 9, 1, 6, 7, 10, 0, 12, 4, 7, 2, 5, 3, 19, 1, 8, 6, 13, 3, 27, 5, 18, 0, 28, 19, 36, 4, 21, 22, 11, 2, 57, 16, 24, 9, 37, 8, 30, 1, 15, 25, 31, 6, 39, 13, 22, 3, 16, 9, 64, 5, 23, 18, 14, 0, 55, 10, 20, 8, 46, 12, 58, 4, 25, 21, 17, 7, 73, 11, 26, 2, 40

Offset: 1

Antti Karttunen, Dec 18 2015

Antti Karttunen, Table of n, a(n) for n = 1..6561
Indranil Ghosh, Python program to generate the sequence

One less than A265911.

Cf. A265345, A265352, A265354 (compare the scatter-plot).

a(2n+1) = A265354(n), a(2n) = a(A265352(n)).

cp's OEIS Frontend

A265351 Permutation of nonnegative integers: a(n) = A263272(A263273(n)).

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A265354 Permutation of nonnegative integers: a(n) = A263273(A264985(n)).

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

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

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A265331 One-based row index to A265345.

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

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A265330 Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).

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

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