A365393 -id:A365393 - cp's OEIS frontend

A365431 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364502(i) = A364502(j) for all i, j >= 1, where A364502(n) is the denominator of n / A005940(n).

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

Offset: 1

Antti Karttunen, Sep 07 2023

Restricted growth sequence transform of A364502, or equally, of A365432.
For all i, j: A003602(i) = A003602(j) => a(i) = a(j).
Compare to the scatter plots of A365393 and A365715.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A005940, A364502, A365432.

Cf. also A365393, A365715 (analogous sequence for Doudna variant D(3)).

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };
v365431 = rgs_transform(vector(up_to,n,A364502(n)));
A365431(n) = v365431[n];

A366376 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366375(i) = A366375(j) for all i, j >= 0, where A366375(n) is the denominator of n / A332214(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Oct 08 2023

Restricted growth sequence transform of A366375.

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A332214, A366373, A366375.

Cf. also A365393, A365431, A366286 (compare the scatter plots).

\\ Needs also program from A332214:
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; };
A366375(n) = { my(u=A332214(n)); (u/gcd(n,u)); };
v366376 = rgs_transform(vector(1+up_to,n,A366375(n-1)));
A366376(n) = v366376[1+n];

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).

Original entry on oeis.org

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];

A365715 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365465(i) = A365465(j) for all i, j >= 1, where A365465(n) = A356867(n) / gcd(n, A356867(n)), and A356867 is Sycamore's Doudna variant D(3).

Original entry on oeis.org

1, 1, 1, 2, 3, 1, 4, 1, 1, 5, 6, 2, 7, 4, 3, 7, 8, 1, 9, 5, 4, 10, 11, 1, 3, 8, 1, 12, 13, 5, 14, 12, 6, 9, 15, 2, 16, 16, 7, 9, 17, 4, 18, 19, 3, 20, 21, 7, 22, 3, 8, 10, 23, 1, 5, 14, 9, 24, 25, 5, 26, 27, 4, 28, 29, 10, 30, 31, 11, 10, 32, 1, 33, 21, 3, 34, 35, 8, 36, 15, 1, 37, 38, 12, 37, 38, 13, 39, 40, 5, 1

Offset: 1

Antti Karttunen, Sep 17 2023

Restricted growth sequence transform of A365465.

Compare to the scatter plots of A365431 (analogous sequence for Doudna variant D(2)), and also of A365393 and A365718.

Antti Karttunen, Table of n, a(n) for n = 1..59049

Cf. A356867, A365465.

Cf. also A365431, A365393, A365718.

\\ Needs also program from A356867:
up_to = 59049; \\ = 3^10.
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; };
A365465(n) = (A356867(n)/gcd(n, A356867(n)));
v365715 = rgs_transform(vector(up_to,n,A365465(n)));
A365715(n) = v365715[n];

A365384 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351251(i) = A351251(j) for all i, j >= 0, where A351251(n) is the denominator of n / A276086(n).

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 7, 8, 7, 4, 9, 10, 11, 12, 7, 13, 14, 15, 16, 12, 16, 17, 18, 19, 11, 20, 21, 22, 23, 24, 25, 26, 25, 27, 5, 28, 29, 30, 29, 27, 31, 10, 32, 33, 29, 34, 35, 36, 16, 30, 37, 38, 39, 40, 37, 20, 41, 42, 43, 44, 45, 46, 25, 47, 48, 49, 50, 51, 50, 27, 52, 53, 54, 55, 45, 56, 35, 57, 58, 55, 58, 59, 60, 40, 58, 61, 62, 63, 64, 65, 45

Offset: 0

Antti Karttunen, Sep 07 2023

nonn

Restricted growth sequence transform of A351251, or equally, of A351253.

Antti Karttunen, Table of n, a(n) for n = 0..65537

Cf. A276086, A351251, A351253.

Cf. also A365393, A365431.

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; };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A351251(n) = denominator(n/A276086(n));
v365384 = rgs_transform(vector(1+up_to,n,A351251(n-1)));
A365384(n) = v365384[1+n];

cp's OEIS Frontend

A365431 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364502(i) = A364502(j) for all i, j >= 1, where A364502(n) is the denominator of n / A005940(n).

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A366376 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366375(i) = A366375(j) for all i, j >= 0, where A366375(n) is the denominator of n / A332214(n).

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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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A365715 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365465(i) = A365465(j) for all i, j >= 1, where A365465(n) = A356867(n) / gcd(n, A356867(n)), and A356867 is Sycamore's Doudna variant D(3).

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A365384 Lexicographically earliest infinite sequence such that a(i) = a(j) => A351251(i) = A351251(j) for all i, j >= 0, where A351251(n) is the denominator of n / A276086(n).

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