A291763 -id:A291763 - cp's OEIS frontend

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).

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];

A305298 Restricted growth sequence transform of A291763, formed from 2-digits in ternary representation of A291763(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 31 2018

nonn

For all i, j: a(i) = a(j) => A292262(i) = A292262(j).

For all i, j: a(i) = a(j) => A305432(i) = A305432(j).

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

Cf. A245612, A289814, A291763, A292262, A305432.
Cf. also A305296, A305297.
Cf. also A304746, A304748.

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));
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; };
v305298 = rgs_transform(vector(65538,n,A291763(n-1)));
A305298(n) = v305298[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

Antti Karttunen, Jun 01 2018

nonn

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

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

Cf. also A305302.

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];

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)).

A291760 Binary encoding of 2-digits in ternary representation of A254103(n).

Original entry on oeis.org

0, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 5, 0, 3, 0, 1, 4, 7, 2, 1, 4, 5, 0, 9, 0, 1, 4, 5, 0, 1, 2, 1, 8, 9, 2, 13, 0, 3, 6, 1, 4, 7, 0, 9, 0, 3, 4, 17, 4, 7, 8, 1, 8, 11, 2, 9, 12, 15, 2, 1, 4, 5, 6, 1, 20, 23, 2, 17, 4, 5, 6, 25, 0, 1, 10, 5, 8, 11, 0, 1, 8, 9, 12, 13, 0, 1, 2, 17, 0, 1, 4, 5, 8, 9, 0, 33, 8, 9, 12, 13, 16, 17, 0, 1, 16, 17, 2, 21, 0, 3, 6, 17

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, A286632, A286633, A289814, A291759, A291763.

a(n) = A289814(A254103(n)).

A292260 Binary encoding of 0-digits in ternary representation of A245612(n).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 2, 0, 0, 3, 2, 1, 0, 16, 8, 10, 4, 1, 2, 4, 0, 12, 0, 1, 4, 6, 0, 0, 0, 41, 34, 0, 16, 33, 22, 11, 8, 2, 0, 10, 4, 21, 10, 12, 0, 5, 26, 23, 0, 4, 4, 3, 8, 5, 14, 2, 0, 5, 2, 3, 0, 146, 80, 132, 68, 43, 2, 180, 32, 0, 68, 81, 44, 12, 16, 2, 16, 33, 6, 48, 0, 9, 22, 33, 8, 54, 40, 8, 20, 11, 26, 2, 0, 126, 8, 9, 52, 0, 48, 52, 0

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, A291763, A291770, A292261, A292262.

Cf. also A292240, A292260.

a(n) = A291770(A245612(n)).

A292262 Number of trailing 2-digits in ternary representation of A245612(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Sep 12 2017

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

Cf. A007814, A007949, A245612, A291763, A292261 (even bisection subtracted by one).

Cf. also A292242, A292252.

(define (A292262 n) (A007949 (+ 1 (A245612 n))))
(define (A292262 n) (A007814 (+ 1 (A291763 n))))
(define (A292262 n) (cond ((<= n 1) n) ((odd? n) 0) (else (+ 1 (A292261 (/ n 2))))))

a(n) = A007949(1+A245612(n)).
a(n) = A007814(1+A291763(n)).
a(0) = 0, a(1) = 1, after which a(2n) = 1 + A292261(n/2), a(2n+1) = 0.

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));

cp's OEIS Frontend

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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A305298 Restricted growth sequence transform of A291763, formed from 2-digits in ternary representation of A291763(n).

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

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

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A291760 Binary encoding of 2-digits in ternary representation of A254103(n).

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A292260 Binary encoding of 0-digits in ternary representation of A245612(n).

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A292262 Number of trailing 2-digits in ternary representation of A245612(n).

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

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