A278222 -id:A278222 - cp's OEIS frontend

A303779 Restricted growth sequence transform of A278222(A303775(n)).

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

Offset: 0

Antti Karttunen, May 06 2018

nonn

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

Cf. A278222, A303775, A303780.

Cf. also A286602, A302795, A304088.

\\ Needs also code from A303775:
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[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));
write_to_bfile(0,rgs_transform(vector(65538,n,A278222(A303775(n-1)))),"b303779.txt");

For all i, j: a(i) = a(j) => A303780(i) = A303780(j).

A304088 Restricted growth sequence transform of A278222(A304083(n)).

Original entry on oeis.org

1, 2, 3, 2, 4, 3, 2, 5, 6, 4, 3, 2, 7, 5, 7, 5, 8, 6, 4, 3, 2, 9, 7, 5, 10, 7, 5, 9, 7, 5, 11, 12, 7, 13, 9, 4, 3, 2, 8, 6, 7, 5, 14, 9, 7, 5, 13, 10, 7, 5, 10, 7, 14, 9, 7, 5, 15, 11, 15, 11, 16, 15, 11, 9, 7, 12, 8, 6, 4, 3, 2, 17, 14, 9, 7, 5, 18, 14, 9, 7, 5, 19, 13, 9, 7, 5, 20, 15, 11, 18, 13, 10, 7, 5, 21, 15, 11, 21, 15, 11, 17, 14, 9, 7, 5

Offset: 0

Antti Karttunen, May 06 2018

nonn

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

Cf. A278222, A304083, A304089.

Cf. also A303779.

\\ Needs also code from A304083:
rgs_transform(invec) = { my(occurrences = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(occurrences,invec[i]), my(pp = mapget(occurrences, invec[i])); outvec[i] = outvec[pp] , mapput(occurrences,invec[i],i); outvec[i] = u; u++ )); outvec; };
write_to_bfile(start_offset,vec,bfilename) = { for(n=1, length(vec), write(bfilename, (n+start_offset)-1, " ", vec[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));
write_to_bfile(0,rgs_transform(vector(65538,n,A278222(A304083(n-1)))),"b304088.txt");

For all i, j: a(i) = a(j) => A304089(i) = A304089(j).

A305431 Restricted growth sequence transform of A278222(A305295(n)), constructed from runlengths of 1-digits in base-3 representation of A245612(n).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jun 01 2018

nonn

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

Cf. A245612, A278222, A305295, A305296, A305432, A305433.

Cf. also A305301.

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));
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; };
v305431 = rgs_transform(vector(65538,n,A278222(A305295(n-1))));
A305431(n) = v305431[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];

A324345 Lexicographically earliest positive sequence such that a(i) = a(j) => A005811(i) = A005811(j) and A278222(i) = A278222(j), for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Feb 24 2019

nonn

Restricted growth sequence transform of the ordered pair [A005811(n), A278222(n)], or equally, of [A005811(n), A286622(n)].
For all i, j >= 1:
  a(i) = a(j) => A033264(i) = A033264(j).

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A005811, A278222, A286622.

Cf. also A033264, A323889, A324343, A324346.

up_to = 65537;
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; };
A005811(n) = hammingweight(bitxor(n, n>>1)); \\ From A005811
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));
Aux324345(n) = [A005811(n), A278222(n)];
v324345 = rgs_transform(vector(1+up_to,n,Aux324345(n-1)));
A324345(n) = v324345[1+n];

a(2^n) = 3 for all n >= 1.

A324531 Lexicographically earliest sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A318458(n)] for all other numbers, except f(1) = 0.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 10, 9, 11, 12, 2, 4, 13, 9, 14, 15, 16, 17, 10, 18, 19, 20, 21, 17, 22, 23, 2, 4, 7, 9, 24, 15, 16, 17, 25, 15, 26, 27, 28, 29, 30, 31, 10, 18, 32, 33, 34, 27, 35, 36, 37, 38, 39, 40, 41, 31, 42, 43, 2, 4, 44, 9, 7, 15, 45, 17, 46, 15, 47, 27, 48, 27, 49, 31, 50, 51, 51, 27, 52, 53, 54, 55, 56, 27, 57, 58, 59, 55, 60, 61, 10, 9, 48

Offset: 1

Antti Karttunen, Mar 05 2019

nonn

For all i, j:

a(i) = a(j) => A324532(i) = A324532(j).

Cf. A278222, A318458, A324400, A324530, A324532.

up_to = 65537;
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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ This function from Charles R Greathouse IV, Aug 17 2011
A278222(n) = A046523(A005940(1+n));
A318458(n) = bitand(n,sigma(n)-n);
Aux324531(n) = if(1==n,0,[A278222(n), A318458(n)]);
v324531 = rgs_transform(vector(up_to,n,Aux324531(n)));
A324531(n) = v324531[n];

For n >= 1, a(2^n) = 2.

A336154 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A278222(i) = A278222(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 4, 7, 8, 5, 9, 10, 11, 2, 4, 7, 8, 7, 12, 13, 14, 5, 9, 13, 15, 10, 16, 17, 18, 2, 4, 7, 8, 7, 12, 13, 14, 7, 12, 19, 20, 13, 21, 22, 23, 5, 9, 13, 15, 13, 21, 24, 25, 10, 16, 22, 26, 17, 27, 28, 29, 2, 4, 7, 8, 7, 12, 13, 14, 7, 12, 19, 20, 13, 21, 22, 23, 7, 12, 19, 20, 19, 30, 31, 32, 13, 21, 31, 33, 22, 34, 35, 36, 5, 9, 13, 15, 13, 21, 24, 25, 13, 21

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A007814(1+n), A278222(n)]. Note that A007814(1+n) gives the number of trailing 1-bits in the binary expansion of n.

For all i, j: A324400(i) = A324400(j) => a(i) = a(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences related to binary expansion of n

Cf. A007814, A278222.

Cf. also A286622, A324400, A336153, A336155, A336156.

up_to = 65537;
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; };
A007814(n) = valuation(n,2);
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));
Aux336154(n) = [A007814(1+n), A278222(n)];
v336154 = rgs_transform(vector(up_to, n, Aux336154(n)));
A336154(n) = v336154[n];

A336313 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336125(i)) = A278222(A336125(j)) for all i, j >= 1.

Original entry on oeis.org

1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 3, 3, 2, 2, 3, 2, 2, 4, 3, 2, 2, 2, 3, 3, 2, 2, 5, 2, 2, 3, 3, 2, 2, 2, 3, 4, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 3, 3, 2, 2, 5, 2, 2, 4, 5, 2, 2, 2, 3, 3, 3, 2, 5, 2, 2, 3, 3, 3, 2, 2, 3, 6, 2, 2, 5, 2, 2, 3, 3, 2, 2, 3, 3, 3, 2, 2, 5, 2, 2, 4, 3, 2, 2, 2, 3, 3

Offset: 1

Antti Karttunen, Jul 17 2020

nonn

Restricted growth sequence transform of A278222(A336125(n)).

For all i, j: A336311(i) = A336311(j) => a(i) = a(j) => A336123(i) = A336123(j).

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

Cf. A253553, A278222, A336124, A336125.

Cf. also A292585, A336311, A336312, A336123.

\\ Needs also code from A336124:
up_to = 1024; \\ 65537;
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; };
A253553(n) = if(n<=2,1,my(f=factor(n), k=#f~); if(f[k,2]>1,f[k,2]--,f[k,1] = precprime(f[k,1]-1)); factorback(f));
A336125(n) = if(n<=2,n-1,(1==A336124(n))+(2*A336125(A253553(n))));
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ From A005940
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));
v336313 = rgs_transform(vector(up_to,n,A278222(A336125(n))));
A336313(n) = v336313[n];

A336394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A331410(i) = A331410(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 10 2020

Restricted growth sequence transform of the ordered pair [A278222(n), A331410(n)].

For all i, j: A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j).

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

Cf. A003602, A278222, A324400, A331410, A336392.

Cf. also A286622, A336473.

up_to = 65537;
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; };
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));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336394(n) = [A278222(n), A331410(n)];
v336394 = rgs_transform(vector(up_to, n, Aux336394(n)));
A336394(n) = v336394[n];

A340382 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A291759(i)) = A278222(A291759(j)), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jan 16 2021

nonn

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

Cf. A278222, A291759, A304748, A340381,
Cf. A340377 (positions of ones).
Cf. also A305302.

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));
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; };
v340382 = rgs_transform(vector(up_to,n,A278222(A291759(n))));
A340382(n) = v340382[n];

cp's OEIS Frontend

A303779 Restricted growth sequence transform of A278222(A303775(n)).

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A304088 Restricted growth sequence transform of A278222(A304083(n)).

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A305431 Restricted growth sequence transform of A278222(A305295(n)), constructed from runlengths of 1-digits in base-3 representation of A245612(n).

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PARI

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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PARI

A324345 Lexicographically earliest positive sequence such that a(i) = a(j) => A005811(i) = A005811(j) and A278222(i) = A278222(j), for all i, j >= 0.

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A324531 Lexicographically earliest sequence such that for all i, j >= 1, a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A318458(n)] for all other numbers, except f(1) = 0.

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PARI

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A336154 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A278222(i) = A278222(j), for all i, j >= 1.

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PARI

A336313 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(A336125(i)) = A278222(A336125(j)) for all i, j >= 1.

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A336394 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A331410(i) = A331410(j), for all i, j >= 1.

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