cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A324389 Lexicographically earliest sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A009194(n), A318458(n)] for all other numbers, except f(1) = -1.

Original entry on oeis.org

1, 2, 3, 2, 3, 4, 3, 2, 2, 5, 3, 6, 3, 7, 8, 2, 3, 9, 3, 10, 3, 11, 3, 12, 2, 13, 14, 15, 3, 16, 3, 2, 17, 18, 3, 19, 3, 11, 3, 20, 3, 21, 3, 22, 23, 7, 3, 6, 2, 24, 25, 26, 3, 27, 28, 29, 28, 30, 3, 31, 3, 32, 33, 2, 3, 34, 3, 18, 17, 35, 3, 36, 3, 5, 3, 37, 3, 38, 3, 39, 2, 18, 3, 40, 41, 11, 17, 42, 3, 43, 44, 45, 3, 46, 47, 12, 3, 48, 23, 49, 3, 50, 3
Offset: 1

Views

Author

Antti Karttunen, Mar 05 2019

Keywords

Comments

For all i, j:
A324401(i) = A324401(j) => a(i) = a(j).
Regarding the scatter plot of this sequence, see also comments in A318310. - Antti Karttunen, Feb 04 2020

Links

Crossrefs

Cf. A009194, A318310, A318458, A324390, A324401, A324530, A331744, A331746, A331747.

Programs

  • PARI
    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; };
A009194(n) = gcd(n,sigma(n));
A318458(n) = bitand(n,sigma(n)-n);
Aux324389(n) = if(1==n,-1,[A009194(n), A318458(n)]);
v324389 = rgs_transform(vector(up_to,n,Aux324389(n)));
A324389(n) = v324389[n];

A331743 Lexicographically earliest infinite sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A323901(i) = A323901(j) for all i, j.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 14, 8, 15, 5, 16, 9, 17, 2, 18, 10, 19, 6, 20, 11, 21, 4, 22, 12, 23, 7, 24, 13, 25, 3, 26, 14, 27, 8, 28, 15, 29, 5, 30, 16, 31, 9, 32, 17, 33, 2, 34, 18, 35, 10, 36, 19, 37, 6, 38, 20, 39, 11, 40, 21, 41, 4, 42, 22, 43, 12, 44, 23, 45, 7, 46, 24, 47, 13, 48, 25, 49, 3, 50, 26, 51, 14, 52, 27, 53, 8, 54
Offset: 0

Views

Author

Antti Karttunen, Feb 05 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A002487(n), A002487(A163511(n))].
For all i, j:
a(i) = a(j) => A331748(i) = A331748(j),
a(i) = a(j) => A331749(i) = A331749(j).

Links

Crossrefs

Cf. A002487, A163511, A323901, A324400, A331742, A331744, A331748, A331749.
Differs from A331745 for the first time at n=77, where a(77) = 40, while A331745(77) = 24.
Differs from A103391(1+n) for the first time at n=191, where a(191) = 23, while A103391(192) = 97.

Programs

  • PARI
    \\ Needs also code from A323901.
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; };
Aux331743(n) = [A002487(n), A323901(n)];
v331743 = rgs_transform(vector(1+up_to, n, Aux331743(n-1)));
A331743(n) = v331743[1+n];

Formula

a(2^n) = 2 for all n >= 0.

A331745 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A323901(i) = A323901(j) for all i, j.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 8, 5, 9, 2, 10, 6, 11, 4, 12, 7, 13, 3, 14, 8, 15, 5, 16, 9, 17, 2, 18, 10, 19, 6, 20, 11, 21, 4, 22, 12, 23, 7, 24, 13, 25, 3, 26, 14, 27, 8, 28, 15, 29, 5, 30, 16, 31, 9, 32, 17, 33, 2, 34, 18, 35, 10, 36, 19, 37, 6, 38, 20, 39, 11, 24, 21, 40, 4, 41, 22, 42, 12, 43, 23, 44, 7, 45, 24, 46, 13, 47, 25, 48, 3, 49, 26, 50, 14, 51, 27, 52, 8, 45
Offset: 0

Views

Author

Antti Karttunen, Feb 04 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A278222(n), A323901(n)].

Links

Crossrefs

Cf. A278222, A323901.
Cf. also A324400, A286622, A318310, A324389, A331744, A331746.

Programs

  • PARI
    \\ Needs also code from A323901.
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 };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
Aux331745(n) = [A278222(n),A323901(n)];
v331745 = rgs_transform(vector(1+up_to, n, Aux331745(n-1)));
A331745(n) = v331745[1+n];

Formula

a(2^n) = 2 for all n >= 0.

A331746 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A331166(i) = A331166(j) for all i, j.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 18, 21, 24, 25, 22, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 33, 37, 38, 39, 40, 41, 42, 43, 31, 44, 45, 46, 38, 47, 48, 49, 35, 41, 48, 50, 42, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 63, 71, 72, 73, 74, 75, 76, 66, 77, 78, 79, 80, 81, 82, 83, 56
Offset: 1

Views

Author

Antti Karttunen, Feb 04 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A009194(n), A331166(n)].
For all i, j:
a(i) = a(j) => A331747(i) = A331747(j).

Links

Crossrefs

Cf. A009194, A331166, A331300.
Cf. also A331744, A331747.

Programs

  • PARI
    \\ Needs also code from A331166.
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; };
A009194(n) = gcd(n, sigma(n));
Aux331746(n) = [A009194(n),A331166(n)];
v331746 = rgs_transform(vector(up_to, n, Aux331746(n)));
A331746(n) = v331746[n];

A331747 Lexicographically earliest infinite sequence such that a(i) = a(j) => A009194(i) = A009194(j) and A278222(i) = A278222(j) for all i, j.

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 5, 1, 3, 6, 7, 8, 7, 9, 10, 1, 3, 11, 7, 6, 12, 13, 14, 15, 7, 13, 16, 17, 14, 18, 19, 1, 11, 6, 7, 3, 12, 13, 14, 20, 12, 21, 22, 23, 24, 25, 26, 8, 7, 7, 27, 13, 22, 28, 29, 30, 14, 25, 29, 31, 26, 32, 33, 1, 3, 34, 7, 6, 35, 13, 14, 11, 12, 36, 22, 23, 22, 37, 26, 6, 12, 36, 22, 38, 39, 40, 41, 23, 22, 42, 43, 44, 45, 46, 47, 15, 7, 7, 27, 7
Offset: 1

Views

Author

Antti Karttunen, Feb 04 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A009194(n), A278222(n)].
For all i, j:
A331746(i) = A331746(j) => a(i) = a(j).

Links

Crossrefs

Cf. A009194, A278222.
Cf. also A324400, A286622, A318310, A318311, A324389, A331744, A331745, A331746.

Programs

  • PARI
    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; };
A009194(n) = gcd(n, sigma(n));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1)));
t };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A278222(n) = A046523(A005940(1+n));
Aux331747(n) = [A009194(n),A278222(n)];
v331747 = rgs_transform(vector(up_to, n, Aux331747(n)));
A331747(n) = v331747[n];

Formula

a(2^n) = 1 for all n >= 0.

A331742 Lexicographically earliest infinite sequence such that a(i) = a(j) => A323901(i) = A323901(j) for all i, j.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 3, 4, 4, 1, 7, 5, 8, 3, 9, 6, 10, 2, 11, 3, 10, 4, 5, 4, 12, 1, 13, 7, 14, 5, 15, 8, 16, 3, 17, 9, 18, 6, 19, 10, 20, 2, 17, 11, 18, 3, 9, 10, 21, 4, 22, 5, 8, 4, 22, 12, 12, 1, 23, 13, 24, 7, 25, 14, 26, 5, 27, 15, 28, 8, 19, 16, 29, 3, 30, 17, 31, 9, 32, 18, 33, 6, 34, 19, 33, 10, 35, 20, 36, 2, 35, 17, 37, 11, 38, 18, 14, 3, 34
Offset: 0

Views

Author

Antti Karttunen, Feb 05 2020

Keywords

Comments

Restricted growth sequence transform of function A323901(n) = A002487(A163511(n)).

Links

Crossrefs

Cf. A002487, A163511, A323901.
Cf. also A286378, A305899, A331743, A331744, A331745.

Programs

  • PARI
    \\ Needs also code from A323901.
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; };
v331742 = rgs_transform(vector(1+up_to, n, A323901(n-1)));
A331742(n) = v331742[1+n];

Formula

a(2^n) = 1 for all n >= 0.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.