A291760 -id:A291760 - cp's OEIS frontend

A304746 Restricted growth sequence transform of A291760(n), formed from 2-digits in ternary representation of A254103(n).

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

Offset: 0

Antti Karttunen, May 29 2018

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

Cf. A254103, A289814, A291760.

Cf. also A304740, A304748.

A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291760(n) = A289814(A254103(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; };
v304746 = rgs_transform(vector(65537,n,A291760(n-1)));
A304746(n) = v304746[1+n];

A305302 Restricted growth sequence transform of A278222(A291760(n)), constructed from runlengths of 2-digits in base-3 representation of A254103(n).

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 2, 4, 1, 3, 1, 2, 2, 5, 2, 2, 2, 4, 1, 4, 1, 2, 2, 4, 1, 2, 2, 2, 2, 4, 2, 6, 1, 3, 3, 2, 2, 5, 1, 4, 1, 3, 2, 4, 2, 5, 2, 2, 2, 6, 2, 4, 3, 7, 2, 2, 2, 4, 3, 2, 4, 8, 2, 4, 2, 4, 3, 6, 1, 2, 4, 4, 2, 6, 1, 2, 2, 4, 3, 6, 1, 2, 2, 4, 1, 2, 2, 4, 2, 4, 1, 4, 2, 4, 3, 6, 2, 4, 1, 2, 2

Offset: 0

Antti Karttunen, May 30 2018

For all i, j: A304746(i) = A304746(j) => a(i) = a(j).

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

Cf. A254103, A289814, A291760, A304746.

Cf. also A305301, A305303.

A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813
A291760(n) = A289814(A254103(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; };
v305302 = rgs_transform(vector(65538,n,A278222(A291760(n-1))));
A305302(n) = v305302[1+n];

A305303 Restricted growth sequence transform of ordered pair [A278222(A304760(n)), A278222(A291760(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A254103(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 30 2018

Restricted growth sequence transform of A290093(A254103(n)).

For all i, j: a(i) = a(j) => A286633(i) = A286633(j) => A286632(i) = A286632(j).

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

Cf. A254103, A289813, A289814, A291760, A304740, A304746, A304760.

Cf. also A286632, A286633, A290093, A290094, A305301, A305302.

A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813
A304760(n) = A289813(A254103(n));
A291760(n) = A289814(A254103(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; };
Aux305303(n) = [A278222(A304760(n)), A278222(A291760(n))];
v305303 = rgs_transform(vector(65538,n,Aux305303(n-1)));
A305303(n) = v305303[1+n];

A291759 Binary encoding of 2-digits in ternary representation of A048673(n).

Original entry on oeis.org

0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 5, 0, 3, 4, 1, 0, 1, 0, 1, 0, 5, 2, 9, 6, 7, 8, 5, 2, 7, 4, 1, 2, 1, 0, 1, 4, 3, 2, 1, 4, 1, 6, 9, 2, 3, 0, 17, 10, 13, 4, 13, 0, 23, 4, 9, 8, 5, 0, 13, 2, 9, 8, 1, 10, 3, 0, 1, 12, 3, 0, 1, 0, 11, 2, 5, 12, 5, 2, 1, 10, 9, 4, 1, 8, 11, 14, 17, 4, 5, 0, 5, 0, 15, 0, 33, 6, 21, 16, 25, 6, 11, 8, 25, 16, 3, 8, 45, 8, 9, 4, 17, 8

Offset: 1

Antti Karttunen, Sep 12 2017

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences related to binary expansion of n

Cf. A048673, A286585, A286586, A289814, A291760, A291763.

a(n) = A289814(A048673(n)).

A291763 Binary encoding of 2-digits in ternary representation of A245612(n).

Original entry on oeis.org

0, 1, 1, 0, 1, 0, 3, 0, 1, 8, 1, 6, 5, 4, 1, 2, 1, 10, 23, 16, 1, 2, 13, 10, 9, 2, 7, 0, 1, 0, 3, 2, 1, 70, 21, 24, 45, 4, 33, 52, 1, 36, 3, 20, 25, 10, 21, 0, 17, 18, 5, 0, 13, 16, 3, 12, 1, 8, 1, 4, 5, 2, 5, 0, 1, 32, 139, 74, 41, 208, 49, 0, 89, 108, 11, 130, 65, 18, 103, 4, 1, 8, 73, 4, 5, 112, 41, 16, 49, 72, 19, 38, 41, 20, 1, 8, 33, 0, 35, 86, 9, 38

Offset: 0

Antti Karttunen, Sep 12 2017

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A245612, A285712, A285714, A285715, A285716, A289814, A291759, A291760.

a(n) = A289814(A245612(n)).

A304760 Binary encoding of 1-digits in ternary representation of A254103(n).

Original entry on oeis.org

0, 1, 0, 2, 2, 3, 0, 0, 6, 4, 4, 1, 2, 7, 4, 5, 14, 3, 0, 4, 10, 0, 0, 6, 6, 12, 12, 2, 10, 8, 8, 5, 30, 4, 4, 9, 2, 15, 12, 0, 22, 11, 8, 9, 2, 11, 8, 1, 14, 19, 16, 1, 26, 3, 0, 8, 22, 3, 0, 12, 18, 8, 8, 1, 62, 3, 0, 20, 10, 16, 16, 9, 6, 28, 28, 1, 26, 7, 4, 13, 46, 20, 20, 2, 18, 16, 16, 13, 6, 20, 20, 10, 18

Offset: 0

Antti Karttunen, May 29 2018

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A254103, A289813, A304740 (rgs-transform).

Cf. also A291760.

A254103(n) = if(!n,n,if(!(n%2),(3*A254103(n/2))-1,(3*(1+A254103((n-1)/2)))\2));
A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A304760(n) = A289813(A254103(n));

a(n) = A289813(A254103(n)).

A292240 Binary encoding of 0-digits in ternary representation of A254103(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 12 2017

Antti Karttunen, Table of n, a(n) for n = 0..16384
Index entries for sequences related to binary expansion of n

Cf. A254103, A291760, A291770, A292241, A292242.

Cf. also A292250, A292260.

a(n) = A291770(A254103(n)).

A292242 Number of trailing 2-digits in ternary representation of A254103(n).

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1

Offset: 0

Antti Karttunen, Sep 12 2017

Antti Karttunen, Table of n, a(n) for n = 0..16384

Cf. A007814, A007949, A254103, A291760, A292241 (even bisection subtracted by one).

Cf. also A292252, A292262.

(define (A292242 n) (A007949 (+ 1 (A254103 n))))
(define (A292242 n) (A007814 (+ 1 (A291760 n))))
(define (A292242 n) (cond ((zero? n) n) ((odd? n) 0) (else (+ 1 (A292241 (/ n 2))))))

a(n) = A007949(1+A254103(n)).
a(n) = A007814(1+A291760(n)).
a(0) = 0, after which, a(2n) = 1 + A292241(n/2), a(2n+1) = 0.

cp's OEIS Frontend

A304746 Restricted growth sequence transform of A291760(n), formed from 2-digits in ternary representation of A254103(n).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A305302 Restricted growth sequence transform of A278222(A291760(n)), constructed from runlengths of 2-digits in base-3 representation of A254103(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A305303 Restricted growth sequence transform of ordered pair [A278222(A304760(n)), A278222(A291760(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A254103(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A291759 Binary encoding of 2-digits in ternary representation of A048673(n).

Views

Author

Keywords

Links

Crossrefs

Formula

A291763 Binary encoding of 2-digits in ternary representation of A245612(n).

Views

Author

Keywords

Links

Crossrefs

Formula

A304760 Binary encoding of 1-digits in ternary representation of A254103(n).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula

A292240 Binary encoding of 0-digits in ternary representation of A254103(n).

Views

Author

Keywords

Links

Crossrefs

Formula

A292242 Number of trailing 2-digits in ternary representation of A254103(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula