A366281 -id:A366281 - 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).

A366278 Perfect powers k such that A052409(k) is equal to A052409(A366275(k)).

Original entry on oeis.org

196, 2116, 2500, 3136, 3844, 9409, 15376, 33856, 37636, 40000, 49729, 50176, 58564, 64516, 148225, 150544, 198916, 229441, 231361, 237169, 246016, 255025, 528529, 541696, 543169, 555025, 592900, 602176, 628849, 640000, 654481, 790321, 795664, 801025, 802816, 917764, 925444, 937024, 948676, 984064, 1020100, 1032256

Offset: 1

Antti Karttunen, Oct 06 2023

nonn

Numbers k such that A052409(k) > 1 and A052409(k) = A366281(k).

Conjecture: all terms are squares, and no higher powers occur.

Antti Karttunen, Table of n, a(n) for n = 1..408

Subsequence of A001597, and also by conjecture, of A153158 (thus also of A000290).
Cf. A052409, A366275, A366281.
Cf. also A365805, A365808.

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));
A052409(n) = { my(k=ispower(n)); if(k, k, n>1); };
isA366278(n) = (A052409(n)>1 && A052409(n)==A052409(A366275(n)));

cp's OEIS Frontend

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

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