A366282 -id:A366282 - cp's OEIS frontend

A366275 The Cat's tongue permutation: a(n) = A163511(A057889(n)).

1, 2, 4, 3, 8, 9, 6, 5, 16, 27, 18, 15, 12, 25, 10, 7, 32, 81, 54, 45, 36, 75, 30, 21, 24, 125, 50, 35, 20, 49, 14, 11, 64, 243, 162, 135, 108, 225, 90, 63, 72, 375, 150, 105, 60, 147, 42, 33, 48, 625, 250, 175, 100, 245, 70, 55, 40, 343, 98, 77, 28, 121, 22, 13, 128, 729, 486, 405, 324, 675, 270, 189, 216, 1125

Offset: 0

Antti Karttunen, Oct 06 2023

"Cat's tongue" refers to the look of the scatter plot of this sequence.

Cf. A000040, A000225, A007814, A057889, A163511, A209229, A290251, A366276 (inverse map), A366277 (fixed points of map n -> a(n)), A366278, A366279, A366280, A366281 [= A052409(a(n))], A366282 [= a(n)-n], A366283 [= gcd(n,a(n))].

Cf. also A163511, A253563, A366263 (compare the scatter plots).

A030101(n) = if(n<1,0,subst(Polrev(binary(n)),x,2));
A057889(n) = if(!n,n,A030101(n/(2^valuation(n,2))) * (2^valuation(n, 2)));
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A366275(n) = A163511(A057889(n));

from sympy import prime
def A366275(n):
    if n:
        k, c, m = int(bin(n>>(r:=(~n & n-1).bit_length()))[:1:-1],2)<>= s+1
        return m*prime(c)
    return 1 # Chai Wah Wu, Oct 08 2023

For n >= 0, A001222(a(n)) = A290251(n).
For n >= 1, A007814(a(n)) = A135523(n) = A007814(n) + A209229(n). [Like A163511, also this permutation preserves the 2-adic valuation of n, except when n is a power of two, in which cases that value is incremented by one.]
For n >= 1, a(2*n) = 2*a(n).
For n >= 1, a(A000225(n)) = A000040(n).

A366283 a(n) = gcd(n, A366275(n)), where A366275 is the Cat's tongue permutation.

Original entry on oeis.org

1, 1, 2, 3, 4, 1, 6, 1, 8, 9, 2, 1, 12, 1, 2, 1, 16, 1, 18, 1, 4, 3, 2, 1, 24, 25, 2, 1, 4, 1, 2, 1, 32, 3, 2, 5, 36, 1, 2, 3, 8, 1, 6, 1, 4, 3, 2, 1, 48, 1, 50, 1, 4, 1, 2, 55, 8, 1, 2, 1, 4, 1, 2, 1, 64, 1, 6, 1, 4, 3, 10, 1, 72, 1, 2, 15, 4, 7, 6, 1, 16, 3, 2, 1, 12, 5, 2, 3, 8, 1, 6, 7, 4, 3, 2, 1, 96, 1, 2, 1, 100

Offset: 0

Antti Karttunen, Oct 07 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A057889, A163511, A366275, A366282, A366284, A366285, A366286.

Differs from related A364255 for the first time at n=25, where a(25) = 25, while A364255(25) = 5.

A366283(n) = gcd(n,A366275(n)); \\ Uses the program given in A366275.

a(n) = gcd(n,A366282(n)) = gcd(A366275(n),A366282(n)).

a(n) = n / A366284(n) = A366275(n) / A366285(n).

A366285 a(n) = A366275(n) / gcd(n, A366275(n)), where A366275 is the Cat's tongue permutation.

Original entry on oeis.org

1, 2, 2, 1, 2, 9, 1, 5, 2, 3, 9, 15, 1, 25, 5, 7, 2, 81, 3, 45, 9, 25, 15, 21, 1, 5, 25, 35, 5, 49, 7, 11, 2, 81, 81, 27, 3, 225, 45, 21, 9, 375, 25, 105, 15, 49, 21, 33, 1, 625, 5, 175, 25, 245, 35, 1, 5, 343, 49, 77, 7, 121, 11, 13, 2, 729, 81, 405, 81, 225, 27, 189, 3, 1125, 225, 21, 45, 63, 21, 99, 9, 625, 375, 525

Offset: 0

Antti Karttunen, Oct 07 2023

Denominator of n / A366275(n).

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A057889, A163511, A366275, A366282, A366283, A366284 (numerators), A366286 (rgs-transform).

Cf. also A364492.

A366285(n) = { my(u=A366275(n)); (u/gcd(n,u)); }; \\ Uses the program given in A366275.

a(n) = A366275(n) / A366283(n) = A366275(n) / gcd(n, A366275(n))

A366372 a(n) = A332214(n) - n, where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Original entry on oeis.org

1, 1, 2, 0, 4, 4, 0, 0, 8, 18, 8, 38, 0, 8, 0, -10, 16, 64, 36, 324, 16, 126, 76, 2, 0, 38, 16, 8, 0, -14, -20, 0, 32, 210, 128, 2366, 72, 992, 648, 86, 32, 400, 252, 132, 152, 30, 4, 914, 0, 140, 76, 194, 32, 52, 16, 100, 0, -12, -28, 158, -40, 32, 0, -52, 64, 664, 420, 16740, 256, 7134, 4732, 554, 144, 3014, 1984

Offset: 0

Antti Karttunen, Oct 08 2023

sign

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A332214, A335431 (known positions of 0's), A366373, A366374, A366375, A366376.

Cf. also A364253, A364258, A366282.

PARI
```
A366372(n) = (A332214(n)-n);
```

A366284 a(n) = n / gcd(n, A366275(n)), where A366275 is the Cat's tongue permutation.

Original entry on oeis.org

0, 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 15, 1, 17, 1, 19, 5, 7, 11, 23, 1, 1, 13, 27, 7, 29, 15, 31, 1, 11, 17, 7, 1, 37, 19, 13, 5, 41, 7, 43, 11, 15, 23, 47, 1, 49, 1, 51, 13, 53, 27, 1, 7, 57, 29, 59, 15, 61, 31, 63, 1, 65, 11, 67, 17, 23, 7, 71, 1, 73, 37, 5, 19, 11, 13, 79, 5, 27, 41, 83, 7, 17, 43, 29, 11

Offset: 0

Antti Karttunen, Oct 07 2023

Numerator of n / A366275(n).

Antti Karttunen, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n

Cf. A057889, A163511, A366275, A366282, A366283, A366285 (denominators), A366286.

Cf. also A364491.

A366284(n) = (n/gcd(n,A366275(n))); \\ Uses the program given in A366275.

a(n) = n / A366283(n) = n / gcd(n, A366275(n))

cp's OEIS Frontend

A366275 The Cat's tongue permutation: a(n) = A163511(A057889(n)).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Python

Formula

A366283 a(n) = gcd(n, A366275(n)), where A366275 is the Cat's tongue permutation.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A366285 a(n) = A366275(n) / gcd(n, A366275(n)), where A366275 is the Cat's tongue permutation.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula

A366372 a(n) = A332214(n) - n, where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A366284 a(n) = n / gcd(n, A366275(n)), where A366275 is the Cat's tongue permutation.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula