A304760 -id:A304760 - cp's OEIS frontend

A304740 Restricted growth sequence transform of A304760(n), formed from 1-digits in ternary representation of A254103(n).

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

Offset: 0

Antti Karttunen, May 29 2018

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

Cf. A254103, A289813, A304760.

Cf. also A304746.

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));
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; };
v304740 = rgs_transform(vector(65538,n,A304760(n-1)));
A304740(n) = v304740[1+n];

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

Original entry on oeis.org

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];

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];

A304759 Binary encoding of 1-digits in ternary representation of A048673(n).

Original entry on oeis.org

1, 0, 2, 2, 3, 0, 0, 6, 7, 4, 1, 2, 4, 4, 0, 14, 5, 12, 6, 10, 9, 0, 4, 6, 1, 0, 4, 10, 5, 8, 1, 30, 8, 8, 14, 26, 2, 8, 13, 22, 3, 16, 0, 2, 17, 12, 8, 14, 1, 0, 10, 2, 10, 0, 9, 22, 3, 8, 11, 18, 9, 0, 18, 62, 0, 20, 12, 18, 1, 24, 13, 54, 15, 0, 28, 18, 0, 24, 12, 46, 37, 4, 8, 34, 7, 4, 0, 6, 11, 32, 23, 26, 22, 0

Offset: 1

Antti Karttunen, May 30 2018

Compare the logarithmic scatterplot to those of A291759, A292250 and A304760.

Antti Karttunen, Table of n, a(n) for n = 1..16383
Index entries for sequences related to binary expansion of n

Cf. A048673, A289813, A304758 (rgs-transform), A340381.
Cf. also A291759, A292250, A304760, A305295.
Cf. A340376 (positions of zeros), A340378 (binary weight).

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)); fromdigits(vector(#d, i, if (d[i]==1, 1, 0)), 2); } \\ From A289813
A304759(n) = A289813(A048673(n));

a(n) = A289813(A048673(n)).

A305295 Binary encoding of 1-digits in ternary representation of A245612(n).

Original entry on oeis.org

1, 0, 2, 2, 6, 7, 0, 3, 14, 4, 12, 1, 2, 0, 4, 0, 30, 37, 0, 5, 26, 28, 0, 1, 6, 17, 8, 14, 10, 9, 4, 1, 62, 16, 72, 103, 2, 90, 8, 0, 54, 25, 60, 33, 2, 32, 0, 19, 14, 40, 32, 40, 18, 11, 24, 0, 22, 18, 16, 9, 10, 8, 0, 4, 126, 333, 36, 305, 146, 4, 204, 331, 6, 147, 176, 44, 18, 225, 8, 121, 110, 214, 48, 203, 122, 6, 64, 78, 6, 1

Offset: 0

Antti Karttunen, May 31 2018

Cf. A245612, A289813, A305296 (rgs-transform).
Cf. also A292260, A291763.
Cf. also A304759, A304760.

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));

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A304740 Restricted growth sequence transform of A304760(n), formed from 1-digits in ternary representation of A254103(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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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).

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A304759 Binary encoding of 1-digits in ternary representation of A048673(n).

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A305295 Binary encoding of 1-digits in ternary representation of A245612(n).

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