A278222 -id:A278222 - cp's OEIS frontend

A323889 Lexicographically earliest positive sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A278222(i) = A278222(j), for all i, j >= 0.

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

Offset: 0

Antti Karttunen, Feb 09 2019

Restricted growth sequence transform of the ordered pair [A002487(n), A278222(n)].

Cf. A002487, A278222, A286622, A324400.

Cf. also A103391, A278243, A286378, A318311, A323892, A323897 and A324533 for a "deformed variant".

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; };
A002487(n) = { my(a=1, b=0); while(n>0, if(bitand(n, 1), b+=a, a+=b); n>>=1); (b); }; \\ From A002487
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));
Aux323889(n) = [A002487(n), A278222(n)];
v323889 = rgs_transform(vector(1+up_to,n,Aux323889(n-1)));
A323889(n) = v323889[1+n];

a(2^n) = 2 for all n >= 0.

A336473 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A329697(i) = A329697(j), for all i, j >= 1.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Jul 24 2020

Restricted growth sequence transform of the ordered pair [A278222(n), A329697(n)].

For all i, j: A336460(i) = A336460(j) => a(i) = a(j).

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

Cf. A278222, A329697.

Cf. also A286622, A336394, A336460, A336470, A336471, A336472, A336474.

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));
A329697(n) = if(!bitand(n,n-1),0,1+A329697(n-(n/vecmax(factor(n)[, 1]))));
Aux336473(n) = [A278222(n), A329697(n)];
v336473 = rgs_transform(vector(up_to, n, Aux336473(n)));
A336473(n) = v336473[n];

A290092 Filter based on 2-digits of base-3 expansion: a(n) = A278222(A289814(n)).

Original entry on oeis.org

1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 6, 2, 2, 6, 4, 4, 8, 1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 6, 2, 2, 6, 4, 4, 8, 2, 2, 6, 2, 2, 6, 6, 6, 12, 2, 2, 6, 2, 2, 6, 6, 6, 12, 4, 4, 12, 4, 4, 12, 8, 8, 16, 1, 1, 2, 1, 1, 2, 2, 2, 4, 1, 1, 2, 1, 1, 2, 2, 2, 4, 2, 2, 6, 2, 2, 6, 4, 4, 8, 1, 1, 2, 1

Offset: 0

Antti Karttunen, Jul 25 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..19683

Cf. A278222, A289814, A290091, A290093.

(define (A290092 n) (A278222 (A289814 n)))

a(n) = A278222(A289814(n)).

A292585 Restricted growth sequence transform of A278222(A292385(n)).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Sep 20 2017

nonn

Term a(n) essentially records the run lengths of numbers of form 4k+1 encountered when starting from that node in binary tree A005940 which contains n, and by then traversing towards the root by iterating the map n -> A252463(n). The actual run lengths can be read from the exponents of primes in the prime factorization of A278222(A292385(m)), where m = min_{k=1..n} for which a(k) = a(n). In compound filter A292584 this is combined with similar information about the run lengths of the numbers of the form 4k+3 (A292583).

			When traversing from the root of binary tree A005940 from the node which contains 5, one obtains path 5 -> 3 -> 2 -> 1. Of these numbers, 5 and 1 are of the form 4k+1, while others are not, thus there are two separate runs of length 1: [1, 1]. On the other hand, when traversing from 9 as 9 -> 4 -> 2 -> 1, again only two terms are of the form 4k+1: 9 and 1 and they are not next to each other, so we have the same two runs of one each: [1, 1]. Similarly for n = 7, and n = 10 as neither in path 7 -> 5 -> 3 -> 2 -> 1 nor in path 10 -> 5 -> 3 -> 2 -> 1 are any more 4k+1 terms (compared to the path beginning from 5). Thus a(5), a(7), a(9) and a(10) are all allotted the same value by the restricted growth sequence transform, which in this case is 3.  Note that 3 occurs in this sequence for the first time at n=5, with A292385(5) = 5 and A278222(5) = 6 = 2^1 * 3^1, where those run lengths 1 and 1 are the prime exponents of 6.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Index entries for sequences computed from indices in prime factorization

Cf. A005940, A252463, A278222, A292375, A292385, A292583, A292584.

allocatemem(2^30);
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; };
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 }; \\ 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
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)};
A278222(n) = A046523(A005940(1+n));
A252463(n) = if(!(n%2),n/2,A064989(n));
A292385(n) = if(n<=2,n-1,(if(1==(n%4),1,0)+(2*A292385(A252463(n)))));
write_to_bfile(1,rgs_transform(vector(16384,n,A278222(A292385(n)))),"b292585_upto16384.txt");

A318311 Filter sequence combining A278222(n) and A294898(n).

Original entry on oeis.org

1, 1, 2, 1, 3, 4, 5, 1, 6, 7, 8, 9, 10, 11, 12, 1, 13, 14, 15, 16, 17, 18, 19, 20, 21, 8, 22, 23, 24, 25, 26, 1, 27, 28, 29, 30, 31, 32, 19, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 1, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 10, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 62, 79

Offset: 1

Antti Karttunen, Aug 25 2018

nonn

Restricted growth sequence transform of ordered pair [A278222(n), A294898(n)].

For all i, j: a(i) = a(j) => A318310(i) = A318310(j) => A033879(i) = A033879(j).

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

Cf. A033879, A278222, A286622, A294898, A318310.

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; };
A005187(n) = { my(s=n); while(n>>=1, s+=n); s; };
A294898(n) = (A005187(n)-sigma(n));
A318311aux(n) = [A278222(n), A294898(n)]; \\ Needs also code from A286622.
v318311 = rgs_transform(vector(up_to,n,A318311aux(n)));
A318311(n) = v318311[n];

A336149 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A278222(i) = A278222(j), for all i, j >= 1.

Original entry on oeis.org

1, 2, 3, 2, 4, 5, 6, 2, 7, 8, 9, 5, 10, 11, 12, 2, 13, 14, 15, 8, 16, 17, 18, 5, 19, 20, 21, 11, 22, 23, 24, 2, 25, 26, 27, 14, 28, 29, 30, 8, 31, 32, 33, 17, 34, 35, 36, 5, 37, 38, 39, 20, 40, 41, 42, 11, 43, 44, 45, 23, 46, 47, 48, 2, 49, 50, 51, 26, 52, 53, 54, 14, 55, 56, 34, 29, 57, 58, 59, 8, 60, 61, 62, 32, 63, 64, 65, 17, 66, 67, 68, 35, 69, 70, 71, 5, 72, 27, 73, 38, 74, 75, 76, 20, 77

Offset: 1

Antti Karttunen, Jul 12 2020

nonn

Restricted growth sequence transform of the ordered pair [A278221(n), A278222(n)], i.e., of the ordered pair [A046523(A122111(n)), A046523(A005940(1+n))].

For all i, j: A336146(i) = A336146(j) => a(i) = a(j) => A035531(i) = A035531(j).

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

Cf. A005940, A046523, A064989, A122111, A278221, A278222.

Cf. also A035531, A286621, A286622, A324400, A336146, A336148, A336159.

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); };
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));
A278222(n) = A046523(A005940(1+n));
Aux336149(n) = [A278221(n),A278222(n)];
v336149 = rgs_transform(vector(up_to, n, Aux336149(n)));
A336149(n) = v336149[n];

A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(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, 3, 5, 9, 3, 10, 6, 11, 2, 12, 7, 13, 4, 14, 8, 15, 1, 16, 3, 17, 5, 18, 9, 19, 3, 20, 10, 21, 6, 22, 11, 23, 2, 24, 12, 25, 7, 26, 13, 27, 4, 28, 14, 29, 8, 30, 15, 31, 1, 32, 16, 33, 3, 34, 17, 35, 5, 18, 18, 22, 9, 36, 19, 37, 3, 38, 20, 39, 10, 40, 21, 41, 6, 42, 22, 43, 11, 44, 23, 45, 2, 7, 24, 46, 12, 47, 25, 48, 7, 49

Offset: 1

Antti Karttunen, Jul 24 2020

nonn

Restricted growth sequence transform of the ordered triple [A278222(n), A336158(n), A336466(n)].
For all i, j:
  A324400(i) = A324400(j) => A003602(i) = A003602(j) => a(i) = a(j),
  a(i) = a(j) => A336159(i) = A336159(j),
  a(i) = a(j) => A336470(i) = A336470(j) => A336471(i) = A336471(j),
  a(i) = a(j) => A336472(i) = A336472(j),
  a(i) = a(j) => A336473(i) = A336473(j).

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

Cf. A278222, A336158, A336466.

Cf. A003602, A324400, A336159, A336470, A336471, A336472, 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; };
A000265(n) = (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));
A336158(n) = A046523(A000265(n));
A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
Aux336460(n) = [A278222(n), A336158(n), A336466(n)];
v336460 = rgs_transform(vector(up_to, n, Aux336460(n)));
A336460(n) = v336460[n];

A286240 Compound filter: a(n) = P(A278222(n), A278222(1+n)), where P(n,k) is sequence A000027 used as a pairing function.

Original entry on oeis.org

2, 5, 12, 14, 23, 42, 59, 44, 23, 61, 142, 117, 109, 183, 261, 152, 23, 61, 142, 148, 601, 850, 607, 375, 109, 265, 1093, 939, 473, 765, 1097, 560, 23, 61, 142, 148, 601, 850, 607, 430, 601, 1741, 3946, 2545, 2497, 3463, 2509, 1323, 109, 265, 1093, 1117, 2497, 4525, 5707, 3153, 473, 1105, 4489, 3813, 1969, 3129, 4497, 2144, 23, 61, 142, 148, 601, 850, 607, 430, 601, 1741

Offset: 0

Antti Karttunen, May 07 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..16383
Eric Weisstein's World of Mathematics, Pairing Function

Cf. A000027, A278222, A286241, A286242, A286255.

Cf. A088705 (one of the matches not matched by A278222 alone. Thus also the whole A007814 (A001511) family is included).

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));
A286240(n) = (2 + ((A278222(n)+A278222(1+n))^2) - A278222(n) - 3*A278222(1+n))/2;
for(n=0, 16383, write("b286240.txt", n, " ", A286240(n)));

from sympy import prime, factorint
import math
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def A(n): return n - 2**int(math.floor(math.log(n, 2)))
def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n))
def a005940(n): return b(n - 1)
def P(n):
    f = factorint(n)
    return sorted([f[i] for i in f])
def a046523(n):
    x=1
    while True:
        if P(n) == P(x): return x
        else: x+=1
def a278222(n): return a046523(a005940(n + 1))
def a(n): return T(a278222(n), a278222(n + 1)) # Indranil Ghosh, May 07 2017

(define (A286240 n) (* (/ 1 2) (+ (expt (+ (A278222 n) (A278222 (+ 1 n))) 2) (- (A278222 n)) (- (* 3 (A278222 (+ 1 n)))) 2)))

a(n) = (1/2)*(2 + ((A278222(n)+A278222(1+n))^2) - A278222(n) - 3*A278222(1+n)).

A286252 Compound filter: a(n) = P(A001511(1+n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.

Original entry on oeis.org

1, 5, 2, 18, 2, 23, 7, 59, 2, 23, 16, 94, 7, 80, 29, 195, 2, 23, 16, 94, 16, 467, 67, 355, 7, 80, 67, 706, 29, 302, 121, 672, 2, 23, 16, 94, 16, 467, 67, 355, 16, 467, 436, 1894, 67, 1832, 277, 1331, 7, 80, 67, 706, 67, 1832, 631, 2779, 29, 302, 277, 2704, 121, 1178, 497, 2422, 2, 23, 16, 94, 16, 467, 67, 355, 16, 467, 436, 1894, 67, 1832, 277, 1331, 16, 467, 436

Offset: 0

Antti Karttunen, May 07 2017

nonn

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

Cf. A000027, A001511, A278222, A286162, A286251, A286253, A286254.

A001511(n) = (1+valuation(n,2));
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));
A286252(n) = (2 + ((A001511(1+n)+A278222(n))^2) - A001511(1+n) - 3*A278222(n))/2;
for(n=0, 16384, write("b286252.txt", n, " ", A286252(n)));

from sympy import prime, factorint
import math
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def A(n): return n - 2**int(math.floor(math.log(n, 2)))
def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n))
def a005940(n): return b(n - 1)
def P(n):
    f = factorint(n)
    return sorted([f[i] for i in f])
def a046523(n):
    x=1
    while True:
        if P(n) == P(x): return x
        else: x+=1
def a278222(n): return a046523(a005940(n + 1))
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a001511(n + 1), a278222(n)) # Indranil Ghosh, May 07 2017

(define (A286252 n) (* (/ 1 2) (+ (expt (+ (A001511 (+ 1 n)) (A278222 n)) 2) (- (A001511 (+ 1 n))) (- (* 3 (A278222 n))) 2)))

a(n) = (1/2)*(2 + ((A001511(1+n)+A278222(n))^2) - A001511(1+n) - 3*A278222(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];

cp's OEIS Frontend

A323889 Lexicographically earliest positive sequence such that a(i) = a(j) => A002487(i) = A002487(j) and A278222(i) = A278222(j), for all i, j >= 0.

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A336473 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278222(i) = A278222(j) and A329697(i) = A329697(j), for all i, j >= 1.

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A290092 Filter based on 2-digits of base-3 expansion: a(n) = A278222(A289814(n)).

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A292585 Restricted growth sequence transform of A278222(A292385(n)).

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A318311 Filter sequence combining A278222(n) and A294898(n).

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A336149 Lexicographically earliest infinite sequence such that a(i) = a(j) => A278221(i) = A278221(j) and A278222(i) = A278222(j), for all i, j >= 1.

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A336460 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A278222(n), A336158(n), A336466(n)], for all i, j >= 1.

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A286240 Compound filter: a(n) = P(A278222(n), A278222(1+n)), where P(n,k) is sequence A000027 used as a pairing function.

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A286252 Compound filter: a(n) = P(A001511(1+n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.

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