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 1-3 of 3 results.

A365388 Lexicographically earliest infinite sequence such that a(i) = a(j) => A334867(i) = A334867(i) and A365386(j) = A365386(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, 20, 3, 21, 11, 22, 6, 23, 12, 24, 2, 25, 13, 26, 7, 27, 14, 28, 4, 29, 15, 30, 8, 31, 16, 32, 1, 33, 17, 34, 9, 35, 18, 36, 5, 37, 19, 38, 10, 39, 20, 40, 3, 41, 21, 42, 11, 43, 22, 44, 6, 45, 23, 46, 12, 47, 24, 48, 2, 49, 25, 41
Offset: 1

Views

Author

Antti Karttunen, Sep 07 2023

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A334867(n), A365386(n)], or equally, of the quadruplet [A329697(n), A334204(n), A331410(n), A365385(n)].
For all i, j:
A003602(i) = A003602(j) => a(i) = a(j),
a(i) = a(j) => A334867(i) = A334867(j),
a(i) = a(j) => A335880(i) = A335880(j),
a(i) = a(j) => A365386(i) = A365386(j).

Links

Crossrefs

Cf. A163511, A329697, A331410, A334204, A334867, A335880, A365385, A365386.
Differs from A003602 and A351090 for the first time at n=99, where a(99) = 41, while A003602(99) = A351090(99) = 50.

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; };
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));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A334204(n) = A329697(A163511(n));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
A365385(n) = A331410(A163511(n));
A365388aux(n) = [A329697(n),A334204(n),A331410(n),A365385(n)];
v365388 = rgs_transform(vector(up_to,n,A365388aux(n)));
A365388(n) = v365388[n];

A334867 Lexicographically earliest infinite sequence such that a(i) = a(j) => A329697(i) = A329697(j) and A334204(i) = A334204(j) for all i, j >= 1.

Original entry on oeis.org

1, 1, 2, 1, 3, 2, 4, 1, 5, 3, 6, 2, 6, 4, 6, 1, 7, 5, 8, 3, 8, 6, 9, 2, 5, 6, 8, 4, 8, 6, 10, 1, 11, 7, 9, 5, 9, 8, 12, 3, 13, 8, 14, 6, 11, 9, 15, 2, 15, 5, 13, 6, 9, 8, 9, 4, 15, 8, 16, 6, 8, 10, 17, 1, 12, 11, 14, 7, 14, 9, 18, 5, 11, 9, 19, 8, 20, 12, 21, 3, 14, 13, 12, 8, 22, 14, 21, 6, 12, 11, 14, 9, 14, 15, 15, 2, 23, 15, 14, 5, 11, 13, 12, 6, 14
Offset: 1

Views

Author

Antti Karttunen, Jun 09 2020

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A329697(n), A334204(n)].
For all i, j:
A365388(i) = A365388(j) => a(i) = a(j) => A334873(i) = A334873(j).

Links

Crossrefs

Cf. A000079 (positions of ones), A163511, A329697, A334204, A334873.
Cf. also A318310, A365386, A365388.

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A054429(n) = ((3<<#binary(n\2))-n-1);
A163511(n) = if(!n,1,A005940(1+A054429(n)));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A334204(n) = A329697(A163511(n));
A334867aux(n) = [A329697(n),A334204(n)];
v334867 = rgs_transform(vector(up_to,n,A334867aux(n)));
A334867(n) = v334867[n];

A366791 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366388(j) = A366388(j) and A366788(i) = A366788(j), for all i, j >= 1.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Oct 23 2023

Keywords

Comments

Restricted growth sequence transform of the ordered pair [A366388(n), A366788(n)].
For all i, j >= 1: A003602(i) = A003602(j) => a(i) = a(j).

Links

Crossrefs

Cf. A003602, A366388, A366788.
Cf. also A334867, A365386, A365388 (compare the scatter plots).

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; };
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));
A366388(n) = if(n<=2, 0, if(isprime(n), 1+A366388(primepi(n)), my(f=factor(n)); (apply(A366388, f[, 1])~ * f[, 2])));
Aux366791(n) = [A366388(n), A366388(A163511(n))];
v366791 = rgs_transform(vector(up_to, n, Aux366791(n)));
A366791(n) = v366791[n];
Showing 1-3 of 3 results.

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