A286622 -id:A286622 - cp's OEIS frontend

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.

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];

A351578 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(f(i)) = A007814(f(j)) and A278222(f(i)) = A278222(f(j)), for all i, j >= 1, where f(k) = A109812(k).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Apr 07 2022

Restricted growth sequence transform of the ordered pair [A007814(A109812(n)), A046523(A005940(1+A109812(n)))].
The sequence allots a new distinct number for each newly encountered combination of the 2-adic valuation of A109812 (A351964), and the multiset of the lengths of 1-runs in the odd part of A109812 (A351965). See the examples.
For all i, j: a(i) = a(j) => A352889(i) = A352889(j).

			   n   A109812(n)  [base-2]   A351964(n)           Lengths of       a(n)
                              (# of trailing 0's)  1-runs       (allotted #)
-----+----------------------------------------------------------------------
   1 :          1       [1],  0                    [1]               1
   2 :          2      [10],  1                    [1]               2
   3 :          4     [100],  2                    [1]               3
   4 :          3      [11],  0                    [2]               4
   5 :          8    [1000],  3                    [1]               5
   6 :          5     [101],  0                    [1,1]             6
   7 :         10    [1010],  1                    [1,1]             7
   8 :         16   [10000],  4                    [1]               8
   9 :          6     [110],  1                    [2]               9
  10 :          9    [1001],  0                    [1,1]             6
  11 :         18   [10010],  1                    [1,1]             7
Because the combinations of the multiset of 1-runs in the binary expansion of A109812(n) and the number of trailing zeros in it (A351964) are unique for n = 1 .. 9, a unique increasing number (starting from 1) is allotted for each, and a(n) = n for n <= 9. On the other hand, at n=10, the binary expansion is [1001], for which these two measures are equal to that of binary expansion [101] found first time at n=6, therefore the rgs-transform allots for 10 the same number as for 6, and a(10) = a(6) = 6. At n=11, the binary expansion is [10010], where these two measures coincide with that of [1010] found first time at n=7, therefore a(10) = a(7) = 7.

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences related to binary expansion of n

Cf. A007814, A109812, A278222 (A286622), A351963, A351964, A351965, A352888, A352889.

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; };
v109812 = readvec("b109812_to10e5.txt"); \\ Prepared from b-file data with gawk ' { print $2 } '
up_to = #v109812;
A109812(n) = v109812[n];
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A007814(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
v351578 = rgs_transform(vector(up_to, n, [A007814(A109812(n)), A046523(A005940(1+A109812(n)))]));
A351578(n) = v351578[n];

A366262 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366261(i) = A366261(j) for all i, j >= 0.

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Oct 05 2023

nonn

Restricted growth sequence transform of A366261.

For all i, j >= 0: a(i) = a(j) => A366254(i) = A366254(j).

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

Cf. A366254, A366260, A366261.

Cf. also A286602, A286619, A286622.

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]); };
A209229(n) = (n && !bitand(n,n-1));
A053644(n) = { my(k=1); while(k<=n, k<<=1); (k>>1); };
A303767(n) = if(!n,n,if(A209229(n),n+A303767(n-1),A053644(n)+A303767(n-A053644(n)-1)));
A366260(n) = A005940(1+A303767(n));
A366261(n) = A046523(A366260(n));
v366262 = rgs_transform(vector(1+up_to,n,A366261(n-1)));
A366262(n) = v366262[1+n];

A286533 Restricted growth sequence of A278533 (prime-signature of A253563).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 17 2017

nonn

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

Cf. A046523, A253563, A286531, A286535, A286622.

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])); }
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
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253563(n) = if(n<2,(1+n),if(!(n%2),A253560(A253563(n/2)),A253550(A253563((n-1)/2)))); \\ Would be better if memoized!
A278533(n) = A046523(A253563(n));
write_to_bfile(0,rgs_transform(vector(65538,n,A278533(n-1))),"b286533.txt");

A286535 Restricted growth sequence of A278535 (prime-signature of A253565).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, May 17 2017

nonn

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

Cf. A046523, A253565, A286531, A286533, A286622.

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])); }
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
A061395(n) = if(1==n, 0, primepi(vecmax(factor(n)[, 1]))); \\ After M. F. Hasler's code for A006530.
A253550(n) = if(1==n, 1, (n/prime(A061395(n)))*prime(1+A061395(n)));
A253560(n) = if(1==n, 1, (n*prime(A061395(n))));
A253565(n) = if(n<2,(1+n),if(!(n%2),A253550(A253565(n/2)),A253560(A253565((n-1)/2)))); \\ Would be better if memoized!
A278535(n) = A046523(A253565(n));
write_to_bfile(0,rgs_transform(vector(65538,n,A278535(n-1))),"b286535.txt");

A302795 Restricted growth sequence transform of A278222(A302793(n)).

Original entry on oeis.org

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

Offset: 0

Antti Karttunen, Apr 26 2018

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

Cf. A278222, A302793.

Cf. also A286602, A286622 (compare the scatter-plots).

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 }; \\ After code in 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));
A193231(n) = { my(x='x); subst(lift(Mod(1, 2)*subst(Pol(binary(n), x), x, 1+x)), x, 2) }; \\ From A193231
A302793(n) = if(!n,n,A193231(1+A193231(n-1)));
write_to_bfile(0,rgs_transform(vector(65538,n,A278222(A302793(n-1)))),"b302795.txt");

A304737 Restricted growth sequence transform of A278222(A064413(n)).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, May 18 2018

nonn

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary representation of A064413(n), the n-th term of EKG-sequence. Compare to the scatter plot of A286622.

Cf. A064301, A064413, A278222, A286622.

Cf. also A304738.

\\ Needs also code for A064413.
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));
v304737 = rgs_transform(vector(65539,n,A278222(A064413(n))));
A304737(n) = v304737[n];

A318831 Restricted growth sequence transform of A278222(A000010(n)).

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Sep 04 2018

nonn

Sequence allots a distinct value for each distinct multiset formed from the lengths of 1-runs in the binary expansion of A000010(n).

For all i, j: a(i) = a(j) => A295660(i) = A295660(j).

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

Cf. also A000010, A278222, A295660, A318835.

Compare also with the scatterplots of A286622, A304101 and A318832.

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));
v318831 = rgs_transform(vector(up_to,n,A278222(eulerphi(n))));
A318831(n) = v318831[n];

A322861 Lexicographically earliest such sequence a that a(i) = a(j) => A278222(A285330(i)) = A278222(A285330(j)) for all i, j.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 31 2018

nonn

Restricted growth sequence transform of A278222(A285330(n)).
For all i, j:
  A322806(i) = A322806(j) => a(i) = a(j),
  A322807(i) = A322807(j) => a(i) = a(j),
  a(i) = a(j) => A322862(i) = A322862(j).

Cf. A048675, A278222, A285330, A286622, A322806, A322807, A322862, A322868.

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 };
A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A048675(n) = my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; \\ From A048675
A285328(n) = { my(r); if((n > 1 && !bitand(n,(n-1))), (n/2), r=A007947(n); if(r==n,1,n = n-r; while(A007947(n) <> r, n = n-r); n)); };
A285330(n) = if(moebius(n)<>0,A048675(n),A285328(n));
A278222(n) = A046523(A005940(1+n));
v322861 = rgs_transform(vector(up_to,n,A278222(A285330(n))));
A322861(n) = v322861[n];

A322866 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(A322863(i)) = A046523(A322863(j)) for all i, j.

Original entry on oeis.org

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

Offset: 1

Antti Karttunen, Dec 30 2018

nonn

Restricted growth sequence transform of A046523(A322863(n)).
Equally, restricted growth sequence transform of A278222(A322865(n)).
For all i, j: a(i) = a(j) => A322867(i) = A322867(j).

Cf. A005940, A046523, A122111, A278222, A286622, A322863, A322865, A322867.

up_to = 8192;
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
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)));
A322863(n) = if(!n,1,A005940(1+A122111(n)));
v322866 = rgs_transform(vector(up_to,n,A046523(A322863(n))));
A322866(n) = v322866[n];

cp's OEIS Frontend

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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A351578 Lexicographically earliest infinite sequence such that a(i) = a(j) => A007814(f(i)) = A007814(f(j)) and A278222(f(i)) = A278222(f(j)), for all i, j >= 1, where f(k) = A109812(k).

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A366262 Lexicographically earliest infinite sequence such that a(i) = a(j) => A366261(i) = A366261(j) for all i, j >= 0.

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A286533 Restricted growth sequence of A278533 (prime-signature of A253563).

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A286535 Restricted growth sequence of A278535 (prime-signature of A253565).

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A302795 Restricted growth sequence transform of A278222(A302793(n)).

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A304737 Restricted growth sequence transform of A278222(A064413(n)).

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A318831 Restricted growth sequence transform of A278222(A000010(n)).

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A322861 Lexicographically earliest such sequence a that a(i) = a(j) => A278222(A285330(i)) = A278222(A285330(j)) for all i, j.

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