A304740 -id:A304740

A304746

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

+10
7

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

PROG

(PARI)

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];

CROSSREFS

Cf. A254103, A289814, A291760.

Cf. also A304740, A304748.

KEYWORD

nonn,look

AUTHOR

Antti Karttunen, May 29 2018

STATUS

approved

A304760

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

+10
6

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

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

Index entries for sequences related to binary expansion of n

FORMULA

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

PROG

(PARI)

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));

CROSSREFS

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

Cf. also A291760.

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, May 29 2018

STATUS

approved

A305296

Restricted growth sequence transform of A305295(n), formed from 1-digits in ternary representation of A245612(n).

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

For all i, j: a(i) = a(j) => A305431(i) = A305431(j).

LINKS

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

PROG

(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)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813

A305295(n) = A289813(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; };

v305296 = rgs_transform(vector(65538, n, A305295(n-1)));

A305296(n) = v305296[1+n];

CROSSREFS

Cf. A245612, A289813, A305295, A305431.

Cf. also A305297, A305298.

Cf. also A304758, A304740.

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 31 2018

STATUS

approved

A305301

Restricted growth sequence transform of A278222(A304760(n)), constructed from runlengths of 1-digits in base-3 representation of A254103(n).

+10
5

1, 2, 1, 2, 2, 3, 1, 1, 3, 2, 2, 2, 2, 4, 2, 5, 4, 3, 1, 2, 5, 1, 1, 3, 3, 3, 3, 2, 5, 2, 2, 5, 6, 2, 2, 5, 2, 6, 3, 1, 7, 7, 2, 5, 2, 7, 2, 2, 4, 7, 2, 2, 7, 3, 1, 2, 7, 3, 1, 3, 5, 2, 2, 2, 8, 3, 1, 5, 5, 2, 2, 5, 3, 4, 4, 2, 7, 4, 2, 7, 9, 5, 5, 2, 5, 2, 2, 7, 3, 5, 5, 5, 5, 1, 1, 5, 6, 5, 5, 5, 5, 1, 1, 5, 10, 2

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

For all i, j: A304740(i) = A304740(j) => a(i) = a(j).

LINKS

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

PROG

(PARI)

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));

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; };

v305301 = rgs_transform(vector(65538, n, A278222(A304760(n-1))));

A305301(n) = v305301[1+n];

CROSSREFS

Cf. A254103, A289813, A304740, A304760.

Cf. also A305302, A305303.

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, May 30 2018

STATUS

approved

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).

+10
5

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

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

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

LINKS

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

PROG

(PARI)

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

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];

CROSSREFS

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

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

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, May 30 2018

STATUS

approved

A304758

Restricted growth sequence transform of A304759(n), formed from 1-digits in ternary representation of A048673(n).

+10
4

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..65537

PROG

(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;

A289813(n) = { my (d=digits(n, 3)); from digits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813

A304759(n) = A289813(A048673(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; };

v304758 = rgs_transform(vector(65537, n, A304759(n)));

A304758(n) = v304758[n];

CROSSREFS

Cf. A048673, A289813, A304759.

Cf. also A304740, A304748.

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 30 2018

STATUS

approved

A304750

Restricted growth sequence transform of A292240(n), formed from 0-digits in ternary representation of A254103(n).

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

COMMENTS

For all i, j: a(i) = a(j) => A292241(i) = A292241(j).

LINKS

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

PROG

(PARI)

A254103(n) = if(!n, n, if(!(n%2), (3*A254103(n/2))-1, (3*(1+A254103((n-1)/2)))\2));

A291770(n) = { my(s=0, b=1, d); while(n>2, if(!(n%3), s += b); b <<= 1; n \= 3); (s); };

A292240(n) = A291770(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; };

v304750 = rgs_transform(vector(65538, n, A292240(n-1)));

A304750(n) = v304750[1+n];

CROSSREFS

Cf. A254103, A291770, A292240.

Cf. also A292241, A304740, A304746.

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 30 2018

STATUS

approved