A304758 -id:A304758 - cp's OEIS frontend

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

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)).

A305296 Restricted growth sequence transform of A305295(n), formed from 1-digits in ternary representation of A245612(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 31 2018

nonn

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

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

Cf. A245612, A289813, A305295, A305431.
Cf. also A305297, A305298.
Cf. also A304758, A304740.

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));
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];

A340381 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A304759(i)) = A278222(A304759(j)), for all i, j >= 1.

Original entry on oeis.org

1, 2, 1, 1, 3, 2, 2, 3, 4, 1, 1, 1, 1, 1, 2, 4, 5, 3, 3, 5, 5, 2, 1, 3, 1, 2, 1, 5, 5, 1, 1, 6, 1, 1, 4, 7, 1, 1, 7, 7, 3, 1, 2, 1, 5, 3, 1, 4, 1, 2, 5, 1, 5, 2, 5, 7, 3, 1, 7, 5, 5, 2, 5, 8, 2, 5, 3, 5, 1, 3, 7, 9, 6, 2, 4, 5, 2, 3, 3, 10, 11, 1, 1, 5, 4, 1, 2, 3, 7, 1, 10, 7, 7, 2, 1, 6, 1, 2, 1, 1, 5, 1, 2, 3, 7

Offset: 1

Antti Karttunen, Jan 16 2021

nonn

For all i, j: A304758(i) = A304758(j) => a(i) = a(j) => A340378(i) = A340378(j).

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

Cf. A278222, A304758, A304759, A340378, A340382, A340383.
Cf. A340376 (positions of 2's).
Cf. also A305301.

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;
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; };
v340381 = rgs_transform(vector(up_to,n,A278222(A304759(n))));
A340381(n) = v340381[n];

cp's OEIS Frontend

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

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A305296 Restricted growth sequence transform of A305295(n), formed from 1-digits in ternary representation of A245612(n).

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A340381 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A304759(i)) = A278222(A304759(j)), for all i, j >= 1.

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