A305303 -id:A305303 - cp's OEIS frontend

A305301 Restricted growth sequence transform of A278222(A304760(n)), constructed from runlengths of 1-digits in base-3 representation of A254103(n).

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

Offset: 0

Antti Karttunen, May 30 2018

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

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

Cf. A254103, A289813, A304740, A304760.

Cf. also A305302, A305303.

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
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];

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];

A305433 Restricted growth sequence transform of ordered pair [A278222(A305295(n)), A278222(A291763(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A245612(n).

Original entry on oeis.org

1, 2, 3, 1, 4, 5, 6, 7, 8, 3, 4, 9, 10, 2, 3, 2, 11, 12, 13, 14, 15, 8, 16, 10, 17, 14, 18, 5, 14, 19, 9, 3, 20, 21, 22, 23, 24, 25, 10, 16, 26, 27, 28, 29, 21, 10, 30, 31, 32, 29, 10, 19, 33, 15, 34, 6, 15, 14, 3, 14, 29, 3, 35, 1, 36, 37, 38, 39, 40, 21, 41, 42, 43, 44, 45, 27, 29, 46, 47, 48, 49, 50, 51, 50, 52, 53, 54, 55, 56, 10, 33, 33, 54, 10, 14

Offset: 0

Antti Karttunen, Jun 01 2018

nonn

Restricted growth sequence transform of A290093(A245612(n)).

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

Cf. A245612, A278222, A290093, A290094, A291763, A305295, A305431, A305432, A305434.

Cf. also A305303.

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
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289813
A305295(n) = A289813(A245612(n));
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; };
Aux305433(n) = [A278222(A305295(n)), A278222(A291763(n))];
v305433 = rgs_transform(vector(65538,n,Aux305433(n-1)));
A305433(n) = v305433[1+n];

A340383 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(A304759(n)), A278222(A291759(n))], for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 16 2021

nonn

Restricted growth sequence transform of the ordered pair [A340381(n), A340382(n)], or equally, of the function f(n) = A290093(A048673(n)).

For all i, j: a(i) = a(j) => A286586(i) = A286586(j) => A286585(i) = A286585(j).

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

Cf. A048673, A278222, A290093, A291759, A304759, A340381, A340382, A340684.

Cf. also A290094, A305303.

up_to = 65537;
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;
A289814(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==2, 1, 0)), 2); } \\ From A289814
A291759(n) = A289814(A048673(n));
A289813(n) = { my (d=digits(n, 3)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A304759(n) = A289813(A048673(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; };
Aux340383(n) = [A278222(A291759(n)),A278222(A304759(n))];
v340383 = rgs_transform(vector(up_to,n,Aux340383(n)));
A340383(n) = v340383[n];

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A305301 Restricted growth sequence transform of A278222(A304760(n)), constructed from runlengths of 1-digits in base-3 representation of A254103(n).

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

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A305433 Restricted growth sequence transform of ordered pair [A278222(A305295(n)), A278222(A291763(n))], constructed from runlengths of 1-digits and 2-digits in base-3 representation of A245612(n).

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A340383 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(A304759(n)), A278222(A291759(n))], for all i, j >= 1.

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