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 1-4 of 4 results.

A336933 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j), for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 10 2020

Keywords

Comments

Restricted growth sequence transform of A007733.

Links

Crossrefs

Cf. A007733, A336934, A336935, A336936.

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; };
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
v336933 = rgs_transform(vector(up_to, n, A007733(n)));
A336933(n) = v336933[n];

A336934 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 10 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A007733(n), A336158(n)].
For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

Crossrefs

Cf. A007733, A336158, A336933, A336935, A336936.

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; };
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
Aux336934(n) = [A007733(n), A336158(n)];
v336934 = rgs_transform(vector(up_to, n, Aux336934(n)));
A336934(n) = v336934[n];

A336936 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A007733(n), A329697(n), A331410(n)], for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Aug 11 2020

Keywords

Comments

Restricted growth sequence transform of the triplet [A007733(n), A329697(n), A331410(n)], or equally, of the ordered pair [A007733(n), A335880(n)].
For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

Links

Crossrefs

Cf. A003602, A007733, A329697, A331410, A335880.
Cf. also A324400, A336920, A336933, A336934, A336935.

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; };
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336936(n) = [A007733(n), A329697(n), A331410(n)];
v336936 = rgs_transform(vector(up_to, n, Aux336936(n)));
A336936(n) = v336936[n];

A351452 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A278222(i) = A278222(j) for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Feb 11 2022

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A006530(n), A278222(n)].
For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).

Links

Crossrefs

Cf. A006530, A278222, A286622.
Cf. also A324400, A336935, A351453, A351454.
Differs from A351454 and A351460 for the first time at n=49, where a(49) = 19, while A351454(49) = A351460(49) = 26.

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; };
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
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));
Aux351452(n) = [A006530(n), A278222(n)];
v351452 = rgs_transform(vector(up_to, n, Aux351452(n)));
A351452(n) = v351452[n];
Showing 1-4 of 4 results.

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