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.

A286531 Restricted growth sequence of A278531 (prime-signature of A163511).

Original entry on oeis.org

1, 2, 3, 2, 4, 3, 5, 2, 6, 4, 7, 3, 7, 5, 5, 2, 8, 6, 9, 4, 10, 7, 7, 3, 9, 7, 11, 5, 7, 5, 5, 2, 12, 8, 13, 6, 14, 9, 9, 4, 14, 10, 15, 7, 10, 7, 7, 3, 13, 9, 15, 7, 15, 11, 11, 5, 9, 7, 11, 5, 7, 5, 5, 2, 16, 12, 17, 8, 18, 13, 13, 6, 19, 14, 20, 9, 14, 9, 9, 4, 18, 14, 21, 10, 21, 15, 15, 7, 14, 10, 15, 7, 10, 7, 7, 3, 17, 13, 20, 9, 21, 15, 15, 7, 20, 15
Offset: 0

Views

Author

Antti Karttunen, May 17 2017

Keywords

Links

Crossrefs

Cf. A046523, A163511, A286533, A286535, A286219, A286622, A305433, A305434.

Programs

  • PARI
    rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[n])); }
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A278222(n) = A046523(A005940(1+n));
A054429(n) = ((3<<#binary(n\2))-n-1); \\ After M. F. Hasler, Aug 18 2014
A278531(n) = if(!n,1,A278222(A054429(n)));
write_to_bfile(0,rgs_transform(vector(65538,n,A278531(n-1))),"b286531.txt");

A305431 Restricted growth sequence transform of A278222(A305295(n)), constructed from runlengths of 1-digits in base-3 representation of A245612(n).

Original entry on oeis.org

1, 2, 1, 1, 3, 4, 2, 3, 4, 1, 3, 1, 1, 2, 1, 2, 5, 6, 2, 7, 8, 4, 2, 1, 3, 7, 1, 4, 7, 7, 1, 1, 9, 1, 7, 10, 1, 11, 1, 2, 12, 8, 5, 7, 1, 1, 2, 8, 4, 7, 1, 7, 7, 8, 3, 2, 8, 7, 1, 7, 7, 1, 2, 1, 13, 14, 7, 11, 6, 1, 12, 14, 3, 11, 8, 8, 7, 15, 1, 16, 10, 17, 3, 17, 16, 3, 1, 15, 3, 1, 7, 7, 1, 1, 7, 6, 5, 7, 6, 1, 7, 11, 1, 8, 8, 1
Offset: 0

Views

Author

Antti Karttunen, Jun 01 2018

Keywords

Links

Crossrefs

Cf. A245612, A278222, A305295, A305296, A305432, A305433.
Cf. also A305301.

Programs

  • PARI
    A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A305295(n) = A289813(A245612(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));
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; };
v305431 = rgs_transform(vector(65538,n,A278222(A305295(n-1))));
A305431(n) = v305431[1+n];

A305432 Restricted growth sequence transform of A278222(A291763(n)), constructed from runlengths of 2-digits in base-3 representation of A245612(n).

Original entry on oeis.org

1, 2, 2, 1, 2, 1, 3, 1, 2, 2, 2, 3, 4, 2, 2, 2, 2, 4, 5, 2, 2, 2, 6, 4, 4, 2, 7, 1, 2, 1, 3, 2, 2, 6, 8, 3, 9, 2, 4, 6, 2, 4, 3, 4, 6, 4, 8, 1, 4, 4, 4, 1, 6, 2, 3, 3, 2, 2, 2, 2, 4, 2, 4, 1, 2, 2, 9, 8, 8, 6, 6, 1, 9, 10, 6, 4, 4, 4, 11, 2, 2, 2, 8, 2, 4, 7, 8, 2, 6, 4, 6, 6, 8, 4, 2, 2, 4, 1, 6, 9, 4, 6, 12, 2, 6, 7
Offset: 0

Views

Author

Antti Karttunen, Jun 01 2018

Keywords

Links

Crossrefs

Cf. A245612, A278222, A291763, A305298, A305431, A305433.
Cf. also A305302.

Programs

  • PARI
    A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291763(n) = A289814(A245612(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));
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; };
v305432 = rgs_transform(vector(65538,n,A278222(A291763(n-1))));
A305432(n) = v305432[1+n];

A305434 Restricted growth sequence transform of A285713, formed from the prime signature of A245612(n).

Original entry on oeis.org

1, 2, 2, 2, 3, 2, 4, 5, 2, 6, 3, 5, 2, 6, 2, 3, 3, 2, 6, 6, 2, 3, 3, 2, 6, 7, 2, 3, 8, 6, 2, 2, 3, 3, 9, 2, 2, 10, 3, 11, 6, 2, 12, 7, 3, 3, 9, 3, 3, 9, 2, 13, 3, 2, 6, 14, 3, 9, 2, 3, 6, 3, 6, 5, 3, 3, 12, 11, 3, 11, 3, 2, 7, 15, 3, 3, 7, 16, 2, 3, 2, 3, 3, 3, 2, 9, 3, 10, 3, 3, 6, 12, 3, 6, 3, 3, 17, 6, 3, 9, 6, 6, 2, 2, 3, 6
Offset: 0

Views

Author

Antti Karttunen, Jun 01 2018

Keywords

Links

Crossrefs

Cf. A046523, A245612, A285713.
Cf. also A305433.

Programs

  • PARI
    A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
A254049(n) = A048673((2*n)-1);
A245612(n) = if(n<2,1+n,if(!(n%2),(3*A245612(n/2))-1,A254049(A245612((n-1)/2))));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A285713(n) = A046523(A245612(n));
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; };
v305434 = rgs_transform(vector(65538,n,A285713(n-1)));
A305434(n) = v305434[1+n];
Showing 1-4 of 4 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.