A365431 -id:A365431 - cp's OEIS frontend

A365393 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364492(i) = A364492(j) for all i, j >= 0, where A364492(n) is the denominator of n / A163511(n).

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

Offset: 0

Antti Karttunen, Sep 06 2023

Restricted growth sequence transform of A364492.

Question: Which sets of numbers cause the finite branches that grow off-angle from the rays emanating from the origin in the scatter plot, and why the sudden bends in some of them? Compare also to the scatter plot of A365431.

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

Cf. A000265, A003602, A163511, A364255, A364492.

Cf. also A365384, 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; };
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));
A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };
v365393 = rgs_transform(vector(1+up_to,n,A364492(n-1)));
A365393(n) = v365393[1+n];

For all n >= 1, a(n) = a(2*n) = a(A000265(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];

A365432 a(n) = A156552(A364502(n)), where A364502(n) = A005940(n) / gcd(n, A005940(n)), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 6, 0, 8, 0, 10, 0, 12, 6, 6, 0, 16, 8, 18, 0, 4, 10, 22, 0, 24, 12, 12, 6, 28, 6, 30, 0, 32, 16, 34, 8, 36, 18, 18, 0, 40, 4, 42, 10, 20, 22, 46, 0, 48, 24, 24, 12, 52, 12, 22, 6, 56, 28, 58, 6, 60, 30, 14, 0, 64, 32, 66, 16, 68, 34, 70, 8, 72, 36, 16, 18, 12, 18, 78, 0, 80, 40, 82, 4, 40, 42, 42, 10

Offset: 1

Antti Karttunen, Sep 07 2023

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384

Cf. A005940, A364500, A341520, A365430, A365431 (rgs-transform).

A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res}; \\ From A156552
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)); };
A365432(n) = A156552(A364502(n));

For all n >= 1, a(n) <= n-1 and A341520(a(n), A365430(n)) = n-1.

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];

A366291 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353271(i) = A353271(j) for all i, j >= 1, where A353271(n) is the numerator of n / A005940(1+(3*A156552(n))).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Oct 06 2023

nonn

Restricted growth sequence transform of A353271.

For all i, j: A305800(i) = A305800(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A005940, A156552, A305800, A332449, A353271.

Cf. also 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; };

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
A332449(n) = A005940(1+(3*A156552(n)));
A353271(n) = (n / gcd(n, A332449(n)));
v366291 = rgs_transform(vector(up_to,n,A353271(n)));
A366291(n) = v366291[n];

cp's OEIS Frontend

A365393 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364492(i) = A364492(j) for all i, j >= 0, where A364492(n) is the denominator of n / A163511(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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A365432 a(n) = A156552(A364502(n)), where A364502(n) = A005940(n) / gcd(n, A005940(n)), and A156552 is the inverse of offset-0 version of Doudna-sequence A005940.

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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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A366291 Lexicographically earliest infinite sequence such that a(i) = a(j) => A353271(i) = A353271(j) for all i, j >= 1, where A353271(n) is the numerator of n / A005940(1+(3*A156552(n))).

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