A324400 -id:A324400 - cp's OEIS frontend

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.

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];

A336934 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 10 2020

nonn

Restricted growth sequence transform of the ordered pair [A007733(n), A336158(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. A007733, A336158, A336933, A336935, A336936.

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; };
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
Aux336934(n) = [A007733(n), A336158(n)];
v336934 = rgs_transform(vector(up_to, n, Aux336934(n)));
A336934(n) = v336934[n];

A336936 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A007733(n), A329697(n), A331410(n)], for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Aug 11 2020

nonn

Restricted growth sequence transform of the triplet [A007733(n), A329697(n), A331410(n)], or equally, of the ordered pair [A007733(n), A335880(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, A007733, A329697, A331410, A335880.

Cf. also A324400, A336920, A336933, A336934, A336935.

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; };
A007733(n) = znorder(Mod(2, n/2^valuation(n, 2))); \\ From A007733
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux336936(n) = [A007733(n), A329697(n), A331410(n)];
v336936 = rgs_transform(vector(up_to, n, Aux336936(n)));
A336936(n) = v336936[n];

A351452 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A278222(i) = A278222(j) for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Feb 11 2022

nonn

Restricted growth sequence transform of the ordered pair [A006530(n), A278222(n)].

For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).

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

Cf. A006530, A278222, A286622.
Cf. also A324400, A336935, A351453, A351454.
Differs from A351454 and A351460 for the first time at n=49, where a(49) = 19, while A351454(49) = A351460(49) = 26.

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; };
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
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));
Aux351452(n) = [A006530(n), A278222(n)];
v351452 = rgs_transform(vector(up_to, n, Aux351452(n)));
A351452(n) = v351452[n];

A351454 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Feb 11 2022

nonn

Restricted growth sequence transform of the triplet [A006530(n), A329697(n), A331410(n)], or equally, of the ordered pair [A006530(n), A335880(n)].

For all i, j >= 1: A324400(i) = A324400(j) => a(i) = a(j).

			a(99) = a(121) because 99 = 3^2 * 11 and 121 = 11^2, so they have equal largest prime factor (A006530), and they also agree on A329697(99) = A329697(121) = 4 and on A331410(99) = A331410(121) = 4, therefore they get equal value (which is 51) allotted to them by the restricted growth sequence transform. - _Antti Karttunen_, Feb 14 2022

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

Cf. A006530, A329697, A331410, A335880.
Cf. also A324400, A336936, A351453.
Differs from A351452 for the first time at n=49, where a(49) = 26, while A351452(49) = 19.
Differs from A351460 for the first time at n=121, where a(121) = 51, while A351460(121) = 62.
Differs from A103391(1+n) for the first time after n=1 at n=121, where a(121) = 51, while A103391(122) = 62.

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; };
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
A331410(n) = if(!bitand(n,n-1),0,1+A331410(n+(n/vecmax(factor(n)[, 1]))));
Aux351454(n) = [A006530(n), A329697(n), A331410(n)];
v351454 = rgs_transform(vector(up_to, n, Aux351454(n)));
A351454(n) = v351454[n];

A335421 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335422(i)) = A046523(A335422(j)) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Jun 09 2020

For all i, j: A324400(i) = A324400(j) => a(i) = a(j) => A335420(i) = A335420(j).

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

Cf. A046523, A335420, A335422.

Cf. also A286622, A324400.

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
A054429(n) = ((3<<#binary(n\2))-n-1); \\ From A054429
A163511(n) = if(!n,1,A005940(1+A054429(n)))
A335422(n) = A005940(1+A163511(n));
v335421 = rgs_transform(vector(1+up_to,n,A046523(A335422(n-1))));
A335421(n) = v335421[1+n];

For all n >= 0, a(2^n) = 1.

A336147 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 3, 7, 8, 5, 9, 10, 11, 2, 12, 5, 13, 7, 14, 15, 16, 5, 4, 17, 3, 10, 18, 19, 20, 2, 21, 22, 23, 5, 24, 25, 26, 7, 27, 28, 29, 15, 11, 30, 31, 5, 6, 7, 32, 17, 33, 5, 34, 10, 35, 36, 37, 19, 38, 39, 14, 2, 40, 41, 42, 22, 43, 28, 44, 5, 45, 46, 11, 25, 47, 48, 49, 7, 3, 50, 51, 28, 52, 53, 54, 15, 55, 19, 56, 30, 57, 58, 59, 5, 60, 10, 21, 7, 61, 62, 63, 17, 64

Offset: 1

Antti Karttunen, Jul 12 2020

nonn

Restricted growth sequence transform of the ordered pair [A020639(n), A278221(n)].
For all i, j:
  A324400(i) = A324400(j) => A336146(i) = A336146(j) => a(i) = a(j),
  a(i) = a(j) => A243055(i) = A243055(j),
  a(i) = a(j) => A336150(i) = A336150(j).

Antti Karttunen, Table of n, a(n) for n = 1..65537
Index entries for sequences computed from indices in prime factorization

Cf. A020639, A046523, A122111, A278221.
Cf. also A243055, A286621, A318891, A324400, A336146, A336148, A336149, A336150.
First differs from A322590 at a(70) = 28 instead of 44.

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; };
A020639(n) = if(1==n, n, factor(n)[1, 1]);
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A278221(n) = A046523(A122111(n));
Aux336147(n) = [A020639(n),A278221(n)];
v336147 = rgs_transform(vector(up_to, n, Aux336147(n)));
A336147(n) = v336147[n];

A336151 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A006530(i) = A006530(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A001221(n), A006530(n)]. The first member of pair gives the number of distinct prime divisors of n, and the second member gives its largest prime factor.

For all i, j: A324400(i) = A324400(j) => A286621(i) = A286621(j) => a(i) = a(j).

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

Cf. A001221, A006530.

Cf. also A286621, A324400, A336150, A336152.

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; };
A006530(n) = if(n>1, vecmax(factor(n)[, 1]), 1);
Aux336151(n) = [omega(n), A006530(n)];
v336151 = rgs_transform(vector(up_to, n, Aux336151(n)));
A336151(n) = v336151[n];

A336153 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A009194(i) = A009194(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 1, 4, 5, 2, 1, 6, 3, 7, 1, 6, 8, 2, 1, 9, 3, 6, 1, 6, 5, 10, 1, 6, 3, 11, 1, 4, 12, 2, 13, 6, 3, 2, 1, 6, 5, 14, 1, 4, 3, 7, 13, 6, 15, 7, 1, 2, 16, 6, 1, 4, 5, 17, 1, 6, 3, 10, 1, 6, 18, 2, 1, 4, 3, 6, 13, 6, 5, 9, 1, 6, 3, 7, 1, 4, 15, 6, 1, 6, 3, 11, 1, 6, 19, 7, 1, 20, 21, 7, 1, 6, 22, 10, 1, 2, 16, 2, 1, 4, 5, 6, 13

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A007814(1+n), A009194(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

Cf. A007814, A009194.

Cf. also A324400, A331747, A336154, 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);
A009194(n) = gcd(n, sigma(n));
Aux336153(n) = [A007814(1+n), A009194(n)];
v336153 = rgs_transform(vector(up_to, n, Aux336153(n)));
A336153(n) = v336153[n];

A336157 Lexicographically earliest infinite sequence such that a(i) = a(j) => A318458(i) = A318458(j) and A336158(i) = A336158(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 11 2020

nonn

Restricted growth sequence transform of the ordered pair [A318458(n), A336158(n)].
For all i, j:
  A324400(i) = A324400(j) => a(i) = a(j).
  A324401(i) = A324401(j) => a(i) = a(j).

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

Cf. A000265, A046523, A318458, A324400, A324401, A336158.

Cf. A324389, A324530, A324531, A324532 for other similar constructions (also similar by their scatter plots).

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; };
A000265(n) = (n>>valuation(n,2));
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A336158(n) = A046523(A000265(n));
A318458(n) = bitand(n, sigma(n)-n);
Aux336157(n) = [A318458(n), A336158(n)];
v336157 = rgs_transform(vector(up_to, n, Aux336157(n)));
A336157(n) = v336157[n];

cp's OEIS Frontend

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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A336934 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007733(i) = A007733(j) and A336158(i) = A336158(j), for all i, j >= 1.

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A336936 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A007733(n), A329697(n), A331410(n)], for all i, j >= 1.

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A351452 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j) and A278222(i) = A278222(j) for all i, j >= 1.

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A351454 Lexicographically earliest infinite sequence such that a(i) = a(j) => A006530(i) = A006530(j), A329697(i) = A329697(j) and A331410(i) = A331410(j) for all i, j >= 1.

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A335421 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A335422(i)) = A046523(A335422(j)) for all i, j >= 0.

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A336147 Lexicographically earliest infinite sequence such that a(i) = a(j) => A020639(i) = A020639(j) and A278221(i) = A278221(j), for all i, j >= 1.

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A336151 Lexicographically earliest infinite sequence such that a(i) = a(j) => A001221(i) = A001221(j) and A006530(i) = A006530(j), for all i, j >= 1.

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A336153 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(1+i) = A007814(1+j) and A009194(i) = A009194(j), for all i, j >= 1.

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