A366285 -id:A366285 - cp's OEIS frontend

A366286 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366285(i) = A366285(j) for all i, j >= 0, where A366285(n) is the denominator of n / A366275(n).

1, 2, 2, 1, 2, 3, 1, 4, 2, 5, 3, 6, 1, 7, 4, 8, 2, 9, 5, 10, 3, 7, 6, 11, 1, 4, 7, 12, 4, 13, 8, 14, 2, 9, 9, 15, 5, 16, 10, 11, 3, 17, 7, 18, 6, 13, 11, 19, 1, 20, 4, 21, 7, 22, 12, 1, 4, 23, 13, 24, 8, 25, 14, 26, 2, 27, 9, 28, 9, 16, 15, 29, 5, 30, 16, 11, 10, 31, 11, 32, 3, 20, 17, 33, 7, 34, 18, 35, 6, 36, 13, 19

Offset: 0

Antti Karttunen, Oct 07 2023

Restricted growth sequence transform of A366285.

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A057889, A163511, A366275, A366283, A366285.

Cf. also A365393, A365431 (compare the scatter plots).

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A366285(n) = { my(u=A366275(n)); (u/gcd(n,u)); }; \\ Uses also the program given in A366275.
v366286 = rgs_transform(vector(1+up_to,n,A366285(n-1)));
A366286(n) = v366286[1+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).

A366375 a(n) = A332214(n) / gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

Original entry on oeis.org

1, 2, 2, 1, 2, 9, 1, 1, 2, 3, 9, 49, 1, 21, 1, 1, 2, 81, 3, 343, 9, 7, 49, 25, 1, 63, 21, 35, 1, 15, 1, 1, 2, 81, 81, 343, 3, 1029, 343, 125, 9, 441, 7, 175, 49, 5, 25, 961, 1, 27, 63, 245, 21, 105, 35, 31, 1, 15, 15, 217, 1, 93, 1, 11, 2, 729, 81, 16807, 81, 2401, 343, 625, 3, 3087, 1029, 35, 343, 375, 125, 29791, 9, 49

Offset: 0

Antti Karttunen, Oct 08 2023

Denominator of n / A332214(n).

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

Cf. A332214, A366372, A366373, A366374 (numerators), A366376 (rgs-transform).

Cf. also A364492, A366285.

A366375(n) = (A332214(n)/gcd(n,A332214(n)));

a(n) = A332214(n) / A366373(n) = A332214(n) / gcd(n, A332214(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

A366286 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366285(i) = A366285(j) for all i, j >= 0, where A366285(n) is the denominator of n / A366275(n).

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

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A366375 a(n) = A332214(n) / gcd(n, A332214(n)), where A332214 is the Mersenne-prime fixing variant of permutation A163511.

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PARI

Formula

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

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Programs

PARI

Formula